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Polish MO Finals
1965 Polish MO Finals
4
4
Part of
1965 Polish MO Finals
Problems
(1)
a - b and 2a + 2b + 1 are squares of integers if 2a^2 + a = 3b^2 + b
Source: Polish MO Finals 1965 p4
8/30/2024
Prove that if the integers
a
a
a
and
b
b
b
satisfy the equation
2
a
2
+
a
=
3
b
2
+
b
,
2a^2 + a = 3b^2 + b,
2
a
2
+
a
=
3
b
2
+
b
,
then the numbers
a
ā
b
a - b
a
ā
b
and
2
a
+
2
b
+
1
2a + 2b + 1
2
a
+
2
b
+
1
are squares of integers.
number theory
Perfect Square