5

Part of 2018 Spain Mathematical Olympiad

Problems(1)

Integers that can be expressed as ax+by

Source: Spain Mathematical Olympiad 2018 P5

a, b

be coprime positive integers. A positive integer

n

is said to be weak if there do not exist any nonnegative integers

x, y

ax+by=n

. Prove that if

n

is a weak integer and

n < \frac{ab}{6}

, then there exists an integer

k \geq 2

kn

number theorySpainDiophantine equation