MathDB

Silesian integers

Source: MEMO 2018 T8

September 2, 2018

number theory

Problem Statement

An integer

n

is called silesian if there exist positive integers

a,b

and

c

such that

n=\frac{a^2+b^2+c^2}{ab+bc+ca}.

(a)

prove that there are infinitely many silesian integers.

(b)

prove that not every positive integer is silesian.