Consider the set of positive integers that satisfy .

MATHEMATICS · Multi-part · CBSE · Mathematics · The Baudhayana-Pythagoras Theorem · The Baudhayana-Pythagoras Theorem

Problem

Consider the set of positive integers that satisfy

x^{2}+y^{2}=z^{2}

. (i) Define a primitive Pythagorean triple. (ii) Show, with proper reasoning, that

(9,40,41)

is a primitive Pythagorean triple while

(15,36,39)

is not. (iii) Let

k

be a positive integer such that

k(9,40,41)

is again a Pythagorean triple whose perimeter does not exceed

100

. Find all possible values of

k

and list the corresponding triples.