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2
25/2 (n+2-\sqrt{2n+3})=q^2 1987 Greece MO Grade X p2
25/2 (n+2-\sqrt{2n+3})=q^2 1987 Greece MO Grade X p2
Source:
September 6, 2024
number theory
Perfect Squares
Perfect Square
Problem Statement
Prove that exprssion
A
=
25
2
(
n
+
2
−
2
n
+
3
)
A=\frac{25}{2}(n+2-\sqrt{2n+3})
A
=
2
25
(
n
+
2
−
2
n
+
3
)
,
(
n
∈
N
)
(n\in\mathbb{N})
(
n
∈
N
)
is a perfect square of an integer if exprssion
A
A
A
is an integer .
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