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square number

Source: miklos schweitzer 1992 q5

October 24, 2021
number theoryreal analysiscollege contestsMiklos Schweitzer

Problem Statement

Prove that if the aia_i's are different natural numbers, then ∑j=1naj2∏k≠jaj+akaj−ak\sum_ {j = 1}^n a_j ^ 2 \prod_{k \neq j} \frac{a_j + a_k}{a_j-a_k} is a square number.
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