MathDB

x+y is a divisor of x^2+y^2

Source:

January 11, 2004

special factorizationsnumber theory solvednumber theory

Problem Statement

Let

x

and

y

be two integers not equal to

0

such that

x+y

is a divisor of

x^2+y^2

. And let

\frac{x^2+y^2}{x+y}

be a divisor of

1978

. Prove that

x = y

.
German IMO Selection Test 1979, problem 2