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Junior Balkan MO
2004 Junior Balkan MO
3
3
Part of
2004 Junior Balkan MO
Problems
(1)
Not too difficult.
Source: JbMO 2004, PROBLEM 3
7/20/2004
If the positive integers
x
x
x
and
y
y
y
are such that
3
x
+
4
y
3x + 4y
3
x
+
4
y
and
4
x
+
3
y
4x + 3y
4
x
+
3
y
are both perfect squares, prove that both
x
x
x
and
y
y
y
are both divisible with
7
7
7
.
quadratics
modular arithmetic
number theory proposed
number theory