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number = sum of squares of divisors [Austria Regional Competition 2017, P4]

Source: Austrian Mathematics Olympiad Regional Competition (Qualifying Round) 2017, Problem 4

June 12, 2018

number theorySum of SquaresDivisorsDivisibility

Problem Statement

Determine all integers

n \geq 2

, satisfying

n=a^2+b^2,

where

a

is the smallest divisor of

n

different from

1

and

b

is an arbitrary divisor of

n

. Proposed by Walther Janous