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Poland - Second Round
1966 Poland - Second Round
4
4
Part of
1966 Poland - Second Round
Problems
(1)
a+1 is perfect square if a^2+a = 3b^2
Source: Polish MO second round 1966 p4
8/28/2024
Prove that if the natural numbers
a
a
a
and
b
b
b
satisfy the equation
a
2
+
a
=
3
b
2
a^2+a = 3b^2
a
2
+
a
=
3
b
2
, then the number
a
+
1
a+1
a
+
1
is the square of an integer.
number theory
Perfect Square