MathDB

Let

(a,b,c)

be a Pythagorean triple, i.e. a triplet of positive integers with a^2\plus{}b^2\equal{}c^2.

a)

Prove that \left(\frac{c}{a}\plus{}\frac{c}{b}\right)^2>8.

b)

Prove that there are no integer

n

and Pythagorean triple

(a,b,c)

satisfying \left(\frac{c}{a}\plus{}\frac{c}{b}\right)^2\equal{}n.

Problem Statement