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1
b is integer if a is integer, 2a + a^2= 2b + b^2 (2021 Polish JMO R2 p1)
b is integer if a is integer, 2a + a^2= 2b + b^2 (2021 Polish JMO R2 p1)
Source:
April 8, 2021
number theory
Integer
Problem Statement
The numbers
a
,
b
a, b
a
,
b
satisfy the condition
2
a
+
a
2
=
2
b
+
b
2
2a + a^2= 2b + b^2
2
a
+
a
2
=
2
b
+
b
2
. Prove that if
a
a
a
is an integer,
b
b
b
is also an integer.
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