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1978 IMO Longlists
22
22
Part of
1978 IMO Longlists
Problems
(1)
x+y is a divisor of x^2+y^2
Source:
1/11/2004
Let
x
x
x
and
y
y
y
be two integers not equal to
0
0
0
such that
x
+
y
x+y
x
+
y
is a divisor of
x
2
+
y
2
x^2+y^2
x
2
+
y
2
. And let
x
2
+
y
2
x
+
y
\frac{x^2+y^2}{x+y}
x
+
y
x
2
+
y
2
be a divisor of
1978
1978
1978
. Prove that
x
=
y
x = y
x
=
y
.German IMO Selection Test 1979, problem 2
special factorizations
number theory solved
number theory