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k^2+2m, m^2+2k never both perfect squares 1988 Greece MO Grade XI p4
k^2+2m, m^2+2k never both perfect squares 1988 Greece MO Grade XI p4
Source:
September 7, 2024
number theory
Perfect Squares
Problem Statement
Prove that there are do not exist natural numbers
k
,
m
k, m
k
,
m
such that numbers
k
2
+
2
m
k^2+2m
k
2
+
2
m
,
m
2
+
2
k
m^2+2k
m
2
+
2
k
to be squares of integers.
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