Let and be positive integers such that and

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

Problem

Let

m

and

n

be positive integers such that

m>n

and

m-n=1

. Consider the three integers

m^{2}-n^{2}

2mn

, and

m^{2}+n^{2}

. (i) Prove that these three integers can always represent the sides of a right-angled triangle. (ii) List all distinct triples produced by this relation for which the hypotenuse does not exceed

100

. (iii) For each triple obtained in part (ii), determine whether it is primitive and give justification for your answer.

Related theory

Mathematical Logic
Pythagoras' Theorem
Triangle Properties
Similarity
Baudhayana-Pythagoras theorem

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