MathDB

A=\{7,12\}\cup\{8m+3\mid m\in\mathbb{N}\cup\{16m+4\mid m\in\mathbb{N}\}

Source: Serbia JBMO TST 2017

October 6, 2023

number theory

Problem Statement

Positive integer

q

is the

k{}

-successor of positive integer

n{}

if there exists a positive integer

p{}

such that

n+p^2=q^2

. Let

A{}

be the set of all positive integers

n{}

that have at least a

k{}

-successor, but every

k{}

-successor does not have

k{}

-successors of its own. Prove that

A=\{7,12\}\cup\{8m+3\mid m\in\mathbb{N}\}\cup\{16m+4\mid m\in\mathbb{N}\}.

Back to Problems View on AoPS