---
tag: Q7CAGJHRPD
kind: statement
role: proposition
name: Wilf's conjecture
msc: [11D07]
sources:
  - wikipedia: en:2302444@r1345552326
    locator: Coin problem, section Wilf's conjecture
    note: adopted
    mention: wikipedia://en/2302444#ZSTU
    sections: [Statement]
inventory: [XSMAN0NCR6]
---

## Statement

In 1978, Wilf conjectured that given coprime integers $a_1<a_2<...<a_d$, and their Frobenius number $F$, we have

$$d\geq\frac{F+1}{F+1-g},$$

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