John D. Cook • 6/25/2026

Consecutive Pythagorean triangle sides

This article examines Pythagorean triples where the sides are consecutive integers, specifically cases where a+1=b or b+1=c. It references George Osborne's 1914 paper proving that the sequence of shorter legs for consecutive-leg triples follows a recurrence relation (OEIS A001652) and provides a closed-form solution. It also covers triples where the longer leg and hypotenuse are consecutive, derived from Euclid's formula with m=n+1. The content is mathematical and number-theoretic, relating to computer science algorithms and integer sequences.

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#number theory #Pythagorean Triples #Recurrence Relation