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Miklós Schweitzer
1992 Miklós Schweitzer
5
5
Part of
1992 Miklós Schweitzer
Problems
(1)
square number
Source: miklos schweitzer 1992 q5
10/24/2021
Prove that if the
a
i
a_i
a
i
's are different natural numbers, then
∑
j
=
1
n
a
j
2
∏
k
≠
j
a
j
+
a
k
a
j
−
a
k
\sum_ {j = 1}^n a_j ^ 2 \prod_{k \neq j} \frac{a_j + a_k}{a_j-a_k}
∑
j
=
1
n
a
j
2
∏
k
=
j
a
j
−
a
k
a
j
+
a
k
is a square number.
number theory
real analysis
college contests
Miklos Schweitzer