Prove in a thoroughly written proof that for all integers a  and m, if a and m are the lengths of the sides of a right triangle and m + 1 is the length of the hypotenuse, then a is an odd integer. Please also explain why this problem is interesting to solve. Thank yo

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 33E: Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that...
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Prove in a thoroughly written proof that for all integers  and m, if a and m are the lengths of the sides of a right triangle and m + 1 is the length of the hypotenuse, then a is an odd integer. Please also explain why this problem is interesting to solve. Thank you

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