11 Number theory

See MSC 11 on zbMATH Open.

Name	Tag	Kind	MSC
The integers are a Euclidean domain	000JFQGDXG	statement	11A05
Partition function	001CX45SWQ	definition	11P81
Square-free integer	004JW7A2N5	definition	11A51
Least common multiple	007NPQX34K	concept	11A05
Composite number	008BH74D7R	concept	11A41
Sum of divisors	009QCP5T3Z	definition	11A25
Euler–Mascheroni constant	00C5P9JZBK	object	11Y60
Addition formula for Fibonacci numbers	00CN2F997Q	statement	11B39
−1 is a square modulo p if and only if p is not 3 modulo 4	00DW862T78	statement	11A15
Congruence is compatible with addition	00FWBN7F0Y	statement	11A07
Modular multiplicative inverse	00GXTQMY8Z	definition	11A07
Norm of a Gaussian integer	00HPT88ZX0	definition	11R11
Divisibility rule	00J8E3HX0M	concept	11A63
Positive definite quadratic form	00QN1N6MNT	definition	15A63, 11E04
Divergence of the sum of the reciprocals of the primes	00RA98X2CP	statement	11N05
Hensel's lemma	010QVB71T2	statement	11A07
Recurrence for Bell numbers	0110GBHPPB	statement	11B73
Prime number	01826KMG2H	concept	11A41
Pythagorean triple	01G1WY1GVX	definition	11D09
Periodic continued fraction	01GBHQ5ABF	concept	11A55
Legendre symbol	01J8AMV9RS	definition	11A15
Integers modulo n	01N3AYAA6N	definition	11A07
Residue class	01RSTGNTXG	concept	11A07
Quadratic integer	01VN79T2PR	definition	11R11
Legendre's formula	01WPV9PHN7	statement	11A51
Cassini's identity	01WQZK97Z5	statement	11B39
Existence of prime factorization	020K0X7HVR	statement	11A51
Euclid's theorem	0292EPPPT0	statement	11A41
Prime factorization	02EKEPPJ3R	concept	11A51
Fermat pseudoprime	02M2K4QH9P	definition	11A51
Sum of the roots of unity	02PETK9PQ4	statement	11R18
Multiplicative order	02RRHJ7R98	concept	11A07
Polar form of a quadratic form	02STTYFBVY	definition	15A63, 11E04
Greatest common divisor	02WF878BH1	definition	11A05
Gauss's lemma on quadratic residues	037ACYXB5Z	statement	11A15
Dirichlet convolution	037F589D1D	concept	11A25
Norm on the Gaussian integers	03AN1V4ZFJ	definition	11R11
Generalized Euclid's lemma	03BAREW1Z5	statement	11A05
Modulo operation	03BR7SAX0Q	concept	11A07
P-adic valuation	03HDF50VN4	concept	11A51
Wilson's theorem	03KGGKTB2E	statement	11A07
Integers modulo n	03VFZ2WETT	concept	11A07
Binet's formula	0404D8TN7Y	statement	11B39
Fermat's theorem on sums of two squares	043B3ENSTY	statement	11E25
Every real number has a decimal expansion	047KEVEZ9Q	statement	11A63
Modular exponentiation	04DR5PM25N	concept	11Y16
Modulo operation	04FHQSJCQ5	definition	11A07
Divisor function	04J4Z73J5B	concept	11A25
Dirichlet's approximation theorem	04JAY9DGB7	statement	11J04
Sum of two squares theorem	04NPWJMA6H	statement	11E25
Continued fraction	04P2RJ4WPS	concept	11A55
Chinese remainder theorem for non-coprime moduli	04SJTX9P4N	statement	11A07
Continued fraction expansion of a real number	04VA28F3HB	concept	11A55
P-adic valuation	04VCPS30ZE	definition	11A51
Multiplicativity of the divisor function	04WC36XKV6	statement	11A25
Existence of primitive roots modulo a prime	04XGKK8WQW	statement	11A07
Euclid's lemma	051VYKA1EX	statement	11A05
Fermat numbers are pairwise coprime	05598J0Y8R	statement	11A41
Generating function for partitions	0578PA53VA	statement	11P81
The nth roots of unity	057BH3JC9S	statement	11R18
Zeckendorf's theorem	05DEJR6TGF	statement	11B39
Harmonic numbers grow like log n	05S2GSPMGA	statement	11B83, 26A12
Carmichael number	060ZX7C32T	concept	11A51
Lucas–Lehmer test	061BTYA0RN	statement	11Y11
Goldbach's conjecture	063JNBSMJ0	conjecture	11P32
Repeating decimals are rational	065S5B9HF1	statement	11A63
Mersenne prime	06GPJF9V7M	definition	11A41
Fermat prime	06N6JAZF44	concept	11A41
Units of the Gaussian integers	06RH4XAGRY	statement	11R11
Number of invertible residues modulo n	06RJWZCG95	statement	11A07
Sum of divisors	06TK51263Q	concept	11A25
Converse of Wilson's theorem	06WRV8HFDY	statement	11A51
Simple continued fraction	06XF7BCFFJ	definition	11A55
Decimal expansion	06XY4X9430	definition	11A63
Congruence is compatible with multiplication	072D5G4SK6	statement	11A07
Gaussian integer	074P7C85XH	concept	11R11
Transcendental number	079EGSD32Y	definition	11J81
Lcm of coprime integers	07CZYE06ZJ	statement	11A05
Signature of a quadratic form	07EZA80NEH	concept	15A63, 11E04
Pépin's test	07HXA8KV6F	statement	11Y11
If 2^p − 1 is prime then p is prime	07MMWAXMYD	statement	11A41
Fermat's Last Theorem for n = 3	07NKG38VEG	statement	11D25
Liouville function	07NN4VNYWM	concept	11A25
Möbius inversion formula	07Q4TBTFVB	statement	11A25
Every integer is a square times a square-free integer	080Q3RPKY6	statement	11A51
Irrational number	080T2TXVQV	definition	11J72
Number of prime factors counted with multiplicity	08420828EY	definition	11A25
Fundamental theorem of arithmetic	084HH1NDCB	statement	11A51
P-adic valuation of a product	0850JJMJYZ	statement	11A51
Law of quadratic reciprocity	085MJS6907	statement	11A15
Fermat's right triangle theorem	086BE0J3FZ	statement	11D25
von Mangoldt function	087EMZTHWN	definition	11A25
Chevalley–Warning theorem	08895Q5W96	statement	11T06
Diophantine equation	08B1RTW7VZ	concept	11D99
Cyclotomic polynomial	08KEYFAH66	concept	11T22
Number of distinct prime factors	08RQ62VAVA	concept	11A25
Liouville function	08RQAPXF1T	definition	11A25
Euler's four-square identity	08WTN6SCQ6	statement	11E25
Square-free integer	08X0VCR2NW	concept	11A51
Arithmetic function	09115NQZ07	concept	11A25
Extended Euclidean algorithm	0964YQFSA8	concept	11A05
Divisibility	096PW7Q014	definition	11A05
Discrete logarithm	09B4X51J09	definition	11A07
Sum of the totient over the divisors	09JXE6XMCC	statement	11A25
Cancellation in congruences	09RDZZGJZ9	statement	11A07
Least common multiple	09S5SN35DJ	definition	11A05
Divisibility by 11	09YBMJTNBM	statement	11A63
Jacobi symbol	0ADTQBXRMC	concept	11A15
Prime factorization	0AEKDFCYFA	definition	11A51
Pell's equation	0AF3DANJ76	definition	11D09
Multiplicative function	0AP80TT660	definition	11A25
The Möbius function is the inverse of the constant function 1	0ASC73QEQT	statement	11A25
Totient of a prime power	0AVY8HKBGD	statement	11A25
Gaussian integer	0B268GVX95	definition	11R11
Legendre's three-square theorem	0B64Q7XNE3	statement	11E25
Continued fraction	0BK6JBK58W	definition	11A55
Number of divisors	0BKJT6WG96	definition	11A25
Fermat's little theorem in the form a^p = a	0BMXWXDVJZ	statement	11A07
Z[√-5] is not a UFD	0BSJYCG7NM	counterexample	11R11
Recurrence for Stirling numbers of the second kind	0C019SDTER	statement	11B73
pi	0C1VYVNV2N	object	11Y60, 33B10
Euler product formula	0C3PN4075R	statement	11M06
Integers	0C4JS9RF5M	object	11A99
Recurrence for Stirling numbers of the first kind	0C5BFX94J9	statement	11B73
Möbius function	0C8QENHYZW	definition	11A25
Greatest common divisor	0C8WYW4KYQ	concept	11A05
Modular multiplicative inverse	0CEC45PRJN	concept	11A07
Classification of complex quadratic forms	0CEX9BRXRZ	statement	11E04, 15A63
exp(2 pi i/n) is a primitive root of unity	0CF0XGYHNJ	statement	11R18
Division algorithm	0CHQKZFK5S	statement	11A05
Partition function	0CV69WDRXW	concept	11P81
Fibonacci recurrence	0D0SMQYEJA	statement	11B39
Harmonic number	0D2Y6G4C4S	definition	11B83
Consecutive Fibonacci numbers are coprime	0D3PFXEAKF	statement	11B39
Convergents of a continued fraction	0D474C7ES1	concept	11A55
Euler's totient function	0DAMHCT17R	concept	11A25
Quadratic residue	0DKCECSYCF	concept	11A15
Bézout's identity	0DQVHMYAGA	statement	11A05
Irrationality of the square root of 2	0DZGSDHD92	statement	11J72
Irrational number	0DZXAXEJQ9	concept	11J72
Number of nth roots of unity	0E021GF2B8	statement	11R18
Primitive root theorem	0E0DNQK22P	statement	11A07
Complete residue system	0E22JKS4W4	definition	11A07
Convergents converge to the number	0E70M92FE3	statement	11A55
Fermat's Last Theorem for n = 4	0E741HSMJ1	statement	11D25
Casting out nines	0E7W0EM6J6	concept	11A63
A composite number has a prime factor at most its square root	0EB6BBMQMC	statement	11A51
Proof by infinite descent	0EFYCFHYFG	concept	11D99
Primality test	0EGJZHZ02C	concept	11Y11
Prime number theorem	0EHBY5Y84N	statement	11N05
Primitive root of unity	0EHM5ZP5QH	concept	11R18
Existence of nontrivial solutions of Pell's equation	0EM6C9SZN5	statement	11D09
Divisibility by 9	0ESHD7ZQDX	statement	11A63
Primitive root modulo n	0F33KX9Q6F	concept	11A07
Mersenne prime	0F3Z22M2GT	concept	11A41
Divisors of a natural number	0F4JSQE2EK	concept	11A05
Quadratic integer	0F4WRWBZZC	concept	11R11
Group of units of Z/nZ	0F8X8ZRQ53	object	11A07, 20K01
Möbius function	0FANE7P0DY	concept	11A25
Divisors of a natural number	0FCWA16FZE	definition	11A05
Twin prime conjecture	0FER36N8SB	conjecture	11N05
Bertrand's postulate	0FJTGZA4GS	statement	11N05
Chinese remainder theorem	0FNN9B4W64	statement	11A07
Multiplicativity of the totient function	0FSJA9M43W	statement	11A25
Deficient number	0G01TS1RRP	definition	11A25
Transcendence of pi	0G0F7FGCGP	statement	11J81
Fibonacci sequence	0GA9K57A39	example	11B39
Coprime integers	0GFKP8F8AG	definition	11A05
Mersenne number	0GJBJ19NXR	definition	11A41
Dirichlet's theorem on arithmetic progressions	0GNVN3CA2P	statement	11N13
Complete residue system	0GPBVKE31D	concept	11A07
Completely multiplicative function	0GS27TKF1V	definition	11A25
Gaussian prime	0GTEHJQRFK	definition	11R11
Units of Z/nZ are the residues coprime to n	0GXNHEHQNA	statement	11A07, 20K01
Arithmetic function	0H2EPRZC0D	definition	11A25
Induction on the integers	0HBS1F00DN	statement	11A99
Discrete logarithm	0HJHYMGN3C	concept	11A07
Reduced residue system	0HV01NH20W	concept	11A07
Totient of a prime	0HY1MXMEN9	statement	11A25
Polar form of a quadratic form	0HYFWKKY3C	concept	15A63, 11E04
Norm of a Gaussian integer	0HYRJF4WNQ	concept	11R11
Quadratic form	0HZNE5QZDJ	definition	15A63, 11E04
Reduced residue system	0J0QEN1DZR	definition	11A07
Liouville number	0J1R5NP36S	definition	11J81
Solutions of Pell's equation are powers of the fundamental solution	0J1TT091TN	statement	11D09
Congruence is compatible with powers	0J5VGJYYC3	statement	11A07
Primitive root of unity	0J817RTVG6	definition	11R18
Stirling numbers of the second kind	0JCQGPY8Z4	concept	11B73
Lindemann–Weierstrass theorem	0JNCBFMPXR	statement	11J81
Legendre symbol	0JTC045NNZ	concept	11A15
Legendre's theorem on continued fractions	0JXTQ392ZM	statement	11J70
Lifting-the-exponent lemma	0JYF6PTKEW	statement	11A51
Brahmagupta–Fibonacci identity	0K2DMACEZ4	statement	11E25
Minkowski's theorem	0K387S2PKQ	statement	11H06
Gaussian integers	0K5W69AC0J	object	11R11
Bernoulli number	0KC00K7KY4	concept	11B68
Fundamental solution of Pell's equation	0KCYJSB9FW	definition	11D09
Classification of Pythagorean triples	0KF3J2KAER	statement	11D09
Dirichlet convolution	0KH1N66QWW	definition	11A25
Primitive root modulo n	0KM2CJ80G7	definition	11A07
Signature of a quadratic form	0KQZYGEJTF	definition	15A63, 11E04
Symmetric bilinear form associated with a quadratic form	0KRVRV5V80	concept	15A63, 11E04
Number of prime factors counted with multiplicity	0KXQKES075	concept	11A25
Stirling numbers of the first kind	0KY7GS695G	concept	11B73
Lagrange's four-square theorem	0KYYSMEVHH	statement	11E25
Fermat's little theorem	0M25PRN3WQ	statement	11A07
Existence of inverses modulo n	0M67FWZWPQ	statement	11A07
Pythagorean triple	0M7ARED5Q7	concept	11D09
Euler's criterion	0M7DEDKSYB	statement	11A15
Algebraic number	0MB4TGMXG6	definition	11R04
Algebraic number	0MNF0BYFQC	concept	11R04
e	0MVCFMW7S4	object	11Y60
Natural numbers	0MWKJ44V5A	object	11A99
Deficient number	0MXFJ0J00R	concept	11A25
Perfect number	0MXGYCH4SY	concept	11A25
Irrationality of square roots of non-squares	0N10YRNNWV	statement	11J72
Composite number	0N3ADXHNTQ	definition	11A41
Liouville's theorem on Diophantine approximation	0N3WFZEFPM	statement	11J68
Fermat primality test	0N5ZSZMYH6	concept	11Y11
Fermat prime	0N9E4G2P97	definition	11A41
Harmonic number	0NANDX7V02	concept	11B83
Rational numbers	0NCJ5WXN6Z	object	11A99
von Mangoldt function	0NK8JTE1NN	concept	11A25
0.999... equals 1	0NN5JEMTVE	example	11A63
Construction of the integers from the natural numbers	0NS58JP68E	concept	11A99
Multiplicative function	0NTWN57GM3	concept	11A25
Z/pZ is a field for p prime	0NV6E43P4A	statement	11A07
Multiplicativity of the Legendre symbol	0NW1JP7TBR	statement	11A15
Divisibility	0PG2H7WKGG	concept	11A05
First supplement to quadratic reciprocity	0PHBS78HKT	statement	11A15
The continued fraction of a rational number terminates	0PMY0YQYXX	statement	11A55
The Gaussian integers are a Euclidean domain	0PN13BB7BT	statement	11R11
Farey sequence	0PN4QJE969	definition	11B57
Dirichlet convolution of multiplicative functions is multiplicative	0PR88XHDMB	statement	11A25
Linear congruence	0PTVNH4GPS	concept	11A07
Liouville number	0PYEZM6CN9	concept	11J81
The algebraic numbers form a field	0QFTETCHKB	statement	11R04
Fundamental solution of Pell's equation	0QG0Q3NDT9	concept	11D09
Irrationality of pi	0QHZX1PK8V	statement	11J72
Residue class	0QRV8FPK5M	definition	11A07
The group of units of Z/pZ is cyclic	0QTHB6PE52	statement	11A07, 20K01
Fermat number	0R03B54V4Z	definition	11A41
Fraction in lowest terms	0R64A2CVN4	statement	11A05
pi is greater than 3	0R7SVNYTJS	statement	11Y60
Integers modulo a prime form a field	0R8YXRC9AJ	statement	11A07
Divisibility by 3	0R9D4CEJEB	statement	11A63
Gcd of Fibonacci numbers	0R9F850CTH	statement	11B39
Linear Diophantine equation	0R9GF3JD0K	concept	11D04
Bernoulli number	0RAS24E1R5	definition	11B68
Quadratic form	0RBQS1JJCR	concept	15A63, 11E04
Positive definite quadratic form	0RP20HFYM3	concept	15A63, 11E04
Prime-counting function	0RQSNVTFVZ	concept	11N05
Gaussian prime	0RVRNR7KA1	concept	11R11
Completely multiplicative function	0RXKW044R4	concept	11A25
Lucas's theorem	0RY4GGMEQG	statement	11B65
Smallest prime factor	0S2SYHTWPY	definition	11A41
Root of unity	0S61N75H45	definition	11R18
Order of the group of units of Z/nZ is Euler's totient	0S7495H4HM	statement	11A07, 11A25
Dirichlet convolution formula	0SAR26CKPS	statement	11A25
Perfect number	0SB7Q8SYSF	definition	11A25
Multiplicative order	0SBRX5CZ5R	definition	11A07
Golden ratio	0SC8T7548D	object	11B39
Continued fraction expansion of a real number	0SJ7Z6VKWK	definition	11A55
Irreducibility of the cyclotomic polynomials over the rationals	0SK1VHZ5R2	statement	11R18
Prime number	0SN0MAEKYX	definition	11A41
Existence of a prime divisor	0SPBEDVNW1	statement	11A41
The Gaussian integers form a Euclidean domain	0SPYEFH7H4	statement	11R11
Quadratic residue	0SQDB87Z3T	definition	11A15
Convergents of a continued fraction	0SRWNR42BQ	definition	11A55
Miller–Rabin primality test	0SZCSYHW60	concept	11Y11
Infinitely many primes congruent to 1 modulo n	0T1BSD7H3M	statement	11N13
Carmichael number	0TA7WT68RK	definition	11A51
Product of the gcd and the lcm	0TDY6JZHKS	statement	11A05
Bell numbers	0TKP3TDD02	concept	11B73
Congruence modulo n	0TPW25CBN6	definition	11A07
Euclidean algorithm	0TRNT4X7J0	concept	11A05
Symmetric bilinear form associated with a quadratic form	0TX2YH2FQS	definition	15A63, 11E04
Frobenius coin problem	0V11FEXK08	statement	11D07
Fibonacci numbers as sums of binomial coefficients	0V4VB6MQDC	statement	11B39
Multiplicativity of the Möbius function	0VB9G5B034	statement	11A25
Kummer's theorem	0VBWK9XYDG	statement	11B65
Euler's theorem	0VC4DVE7DQ	statement	11A07
Abundant number	0VG7VNEWMG	concept	11A25
Decimal expansion	0VM8B2SB4P	concept	11A63
Smallest prime factor	0VMWPGGG3C	concept	11A41
If 2^n + 1 is prime then n is a power of 2	0VN4H8M12X	statement	11A41
Abundant number	0VS0MP1P5H	definition	11A25
Transcendental number	0VTQXTCR2G	concept	11J81
Euler's totient function	0VV04M41AN	definition	11A25
Number of divisors	0VV3ZMRF88	concept	11A25
Coprime integers	0VZ48N083F	concept	11A05
Cyclotomic polynomial	0W0KVBM54S	definition	11T22
Irrationality of e	0W4GQSG7B6	statement	11J72
Fermat pseudoprime	0W93FJAC8F	concept	11A51
Congruence modulo n	0WAY5WX8NY	concept	11A07
Norm on the Gaussian integers	0WBRJXXDPZ	concept	11R11
Euclid–Euler theorem	0WETJCKNRG	statement	11A25
Sylvester's law of inertia	0WFED3K3DQ	statement	15A63, 11E04
Fermat number	0WKG15TV3G	concept	11A41
A prime is a Gaussian prime if and only if it is 3 modulo 4	0WMJSEFYFE	statement	11R11
Bell numbers	0WW85SQVS3	definition	11B73
Simple continued fraction	0XB0J0P64D	concept	11A55
Wallis product	0XCYA4YERS	statement	11Y60
Jacobi symbol	0XDB5AW7M1	definition	11A15
Periodic continued fraction	0XKJPFS2W0	definition	11A55
Sieve of Eratosthenes	0XM8ZA9RNM	concept	11Y11
Farey sequence	0XRDYJQES6	concept	11B57
Prime-counting function	0XRJB5SSNE	definition	11N05
Eisenstein's lemma	0XSDBCP4RZ	statement	11A15
A root of an integer is an integer or irrational	0XWCKJZRYH	statement	11J72
The order modulo p divides p − 1	0Y4B7P0GS8	statement	11A07
Fermat's Last Theorem	0Y5X3SDBCZ	statement	11D41
Mersenne number	0YAG43TCXQ	concept	11A41
Divisor function	0YEW47VJ0J	definition	11A25
Irrationality of the square root of a prime	0YHFMXJJAZ	statement	11J72
Root of unity	0YV2CKP2AV	concept	11R18
Number of distinct prime factors	0YVVXT3A0B	definition	11A25
Quadratic reciprocity for the Jacobi symbol	0YY06KP3ZQ	statement	11A15
Pell's equation	0Z0NE3J6JX	concept	11D09
Stirling numbers of the first kind	0Z22VQH17V	definition	11B73
Diagonalisation of a quadratic form	0Z3FEWZ8HA	statement	11E04, 15A63
Trial division	0Z962ECCXR	concept	11Y05
Stirling numbers of the second kind	0ZN07RQ3JS	definition	11B73
Recursively defined sequence	0ZPV68RN1X	concept	11B37
Second supplement to quadratic reciprocity	0ZXW95S44M	statement	11A15