What question did this study set out to answer?

The aim is to explore the divisibility of the product (a+b)c by the binomial coefficient related to primitive Pythagorean triples.

June 5, 2026Open Access

Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples

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Key Points

The aim is to explore the divisibility of the product (a+b)c by the binomial coefficient related to primitive Pythagorean triples.
Analyzed the relationship between (a+b)c and the binomial coefficient.
Formal proof presented for divisibility conditions.
Integer sequence submitted to the On-Line Encyclopedia of Integer Sequences (OEIS).
Established the specific conditions under which the product (a+b)c divides the binomial coefficient.
Demonstrated the relevance of these conditions to monotone lattice paths.

Abstract

This manuscript investigates an arithmetical and combinatorial property of primitive Pythagorean triples (a,b,c). We analyze the condition under which the product (a+b)c divides the binomial coefficient, which corresponds to the number of monotone lattice paths from (0,0) to (a, b). This document serves as the formal proof and mathematical foundation for the corresponding integer sequence submitted to the On-Line Encyclopedia of Integer Sequences (OEIS).

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Pascal T. Grülling

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Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples

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