Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples (V2)

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).