Math 2.0

Number theory Proposition

Wilf's conjecture

Statement

In 1978, Wilf conjectured that given coprime integers a1<a2<...<ada_1<a_2<...<a_d, and their Frobenius number FF, we have

d≥F+1F+1−g,d\geq\frac{F+1}{F+1-g},

where gg denotes the number of all non-representable positive integers. In 2015, an asymptotic version of this was proven by Moscariello and Sammartano.

Further reading

  1. Wikipedia, page 2302444, revision 1345552326, Coin problem, section Wilf's conjecture. adopted
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