(Solved): Using Number theory 2. This question considers writing 260 as a sum of two squares. (a) Explain why ...

2. This question considers writing 260 as a sum of two squares. (a) Explain why 260 can be written as the sum of two squares. Your answer to this part of the question should not resort to finding such a decomposition. (b) Construct a Gaussian integer $?$ such that $N(?)=260$. Hence give 260 as the sum of two squares. (c) Give an irreducible factorisation of your given $?$. (d) Hence by considering a different product of irreducibles, give a different decomposition of 260 as the sum of two squares.