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ISI 2020 : Problem 7

Source: B.Stat & B.Math Entrance Exam 2020

September 20, 2020
isi2020number theory

Problem Statement

Consider a right-angled triangle with integer-valued sides a<b<ca<b<c where a,b,ca,b,c are pairwise co-prime. Let d=c−bd=c-b . Suppose dd divides aa . Then
(a) Prove that d⩽2d\leqslant 2.
(b) Find all such triangles (i.e. all possible triplets a,b,ca,b,c) with perimeter less than 100100 .
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