Proof of Fermat's Last Theorem for n = 4

Reading path

To understand this page from the ground up, read these 55 pages in order. The foundations come first. The path takes the proofs Proof of Bézout's identity, Proof of the generalized Euclid's lemma, Proof of the commutativity of addition by induction, Proof of the classification of Pythagorean triples, Proof of Fermat's right triangle theorem by infinite descent, Proof of Euclid's lemma, Proof of the geometric formula for the dot product, Proof of strong induction from ordinary induction, Proof that the p-adic valuation of a product is the sum of the valuations, Proof of the fundamental theorem of arithmetic, Proof of the Pythagorean theorem and its converse with the dot product, Proof of the existence of prime factorization, Proof of the well-ordering principle from strong induction, Proof of the division algorithm, Proof of the existence of a prime divisor.

1. Angle at a point concept
2. Angle between two vectors concept
3. Definition by recursion concept
4. Divisibility definition
5. Dot product concept
6. Euclidean distance concept
7. Length of a vector concept
8. Mathematical induction concept
9. Natural numbers object
10. Peano axioms concept
11. Proof by infinite descent concept
12. Triangle concept
13. Greatest common divisor definition
14. Prime number definition
15. Proof of the geometric formula for the dot product proof
16. Successor function definition
17. Coprime integers definition
18. Pythagorean triple definition
19. Prime factorization definition
20. P-adic valuation definition
21. Geometric formula for the dot product statement
22. Addition of natural numbers definition
23. The successor function is injective statement
24. Zero is not a successor statement
25. Vectors are perpendicular if and only if their dot product is zero statement
26. Proof of the commutativity of addition by induction proof
27. Order on the natural numbers definition
28. Commutativity of addition statement
29. Proof of the Pythagorean theorem and its converse with the dot product proof
30. Proof of strong induction from ordinary induction proof
31. Strong induction statement
32. Pythagorean theorem statement
33. Proof of the well-ordering principle from strong induction proof
34. Well-ordering principle statement
35. Proof of the division algorithm proof
36. Proof of the existence of a prime divisor proof
37. Division algorithm statement
38. Existence of a prime divisor statement
39. Proof of Bézout's identity proof
40. Proof of the existence of prime factorization proof
41. Bézout's identity statement
42. Existence of prime factorization statement
43. Proof of the generalized Euclid's lemma proof
44. Generalized Euclid's lemma statement
45. Proof of Euclid's lemma proof
46. Euclid's lemma statement
47. Proof of the fundamental theorem of arithmetic proof
48. Proof that the p-adic valuation of a product is the sum of the valuations proof
49. Fundamental theorem of arithmetic statement
50. P-adic valuation of a product statement
51. Proof of the classification of Pythagorean triples proof
52. Classification of Pythagorean triples statement
53. Proof of Fermat's right triangle theorem by infinite descent proof
54. Fermat's right triangle theorem statement
55. Proof of Fermat's Last Theorem for n = 4 proof