MathDB

Let positive integers

a,\ b,\ c

be pairwise coprime. Denote by

g(a, b, c)

the maximum integer not representable in the form

xa+yb+zc

with positive integral

x,\ y,\ z

. Prove that

g(a, b, c)\ge \sqrt{2abc}

(M. Ivanov)
[hide="Remarks (containing spoilers!)"] 1. It can be proven that

g(a,b,c)\ge \sqrt{3abc}

. 2. The constant

3

is the best possible, as proved by the equation

g(3,3k+1,3k+2)=9k+5

Problem Statement