MathDB

(a) Write

A = k^4 + 4

, where

k

is a positive integer, as a product of two factors each of them is sum of two squares of integers. (b) Simplify the expression

K=\frac{(2^4+\frac14)(4^4+\frac14)...((2n)^4+\frac14)}{(1^4+\frac14)(3^4+\frac14)...((2n-1)^4+\frac14)}

and write it as sum of squares of two consecutive positive integers

Problem Statement