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Sweden Contests
Swedish Mathematical Competition
1993 Swedish Mathematical Competition
3
3
Part of
1993 Swedish Mathematical Competition
Problems
(1)
a^2 +b^2 +x^2 = y^2 has an integer solution x,y iff product ab is even
Source: 1993 Swedish Mathematical Competition p3
4/2/2021
Assume that
a
a
a
and
b
b
b
are integers. Prove that the equation
a
2
+
b
2
+
x
2
=
y
2
a^2 +b^2 +x^2 = y^2
a
2
+
b
2
+
x
2
=
y
2
has an integer solution
x
,
y
x,y
x
,
y
if and only if the product
a
b
ab
ab
is even.
Even
number theory
diophantine
Diophantine equation