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arXiv · 2508.15781

The problem of finding three numbers such that the sum or difference of any two of them is a square number

Seiji Tomita
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Abstract

Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these solutions. Additionally, we derive two parametric solutions using the elliptic curve method and find all solutions within the range of $10^8$.

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Seiji Tomita. 2025-08-05. The problem of finding three numbers such that the sum or difference of any two of them is a square number. https://arxiv.org/abs/2508.15781

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