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N3
a-b square if 2a^2 + a = 3b^2 + b OLCOMA Costa Rica 2018 SL N3
a-b square if 2a^2 + a = 3b^2 + b OLCOMA Costa Rica 2018 SL N3
Source:
October 1, 2021
number theory
diophantine
Problem Statement
Let
a
a
a
and
b
b
b
be positive integers such that
2
a
2
+
a
=
3
b
2
+
b
2a^2 + a = 3b^2 + b
2
a
2
+
a
=
3
b
2
+
b
. Prove that
a
ā
b
a-b
a
ā
b
is a perfect square.
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