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. inequalitiesnumber theory unsolvednumber theory