4

Part of 2017 Regional Competition For Advanced Students

Problems(1)

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

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

Determine all integers

n \geq 2

n=a^2+b^2,

a

is the smallest divisor of

n

1

b

is an arbitrary divisor of

n

. Proposed by Walther Janous

number theorySum of SquaresDivisorsDivisibility