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

2025/08/05 by Tomita, Seiji
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2508.15781

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 10⁸.

Citations

• Rational points on elliptic curves

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