Question Number 52728 by hassentimol last updated on 12/Jan/19
$${How}\:{can}\:{you}\:{proove}\:{what}\:{follows}\:? \\ $$$$ \\ $$$$\mathrm{If}\:\left(\mathrm{4}{n}+\mathrm{1}\right)\:\mathrm{is}\:\mathrm{prime},\:\mathrm{then}\:: \\ $$$$\:\:\:\mathrm{4}{n}\:+\:\mathrm{1}\:=\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:\:\:\:\mathrm{with}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$$$ \\ $$$${Thank}\:{you} \\ $$