microsoft_office_word 11.02.2018 23:15 Find if there are solutions : $ a,b \in\mathbb{N} $ , $a^2+b^2=2018 $ , $ 7|a+b $ .
mathdragon2000 11.02.2018 23:45 Insight w/ mod 7 To get the above solution more easily, consider the expression $ \pmod 7 $. Then only the case $ a \equiv 1 \pmod{7}, b \equiv 6 \pmod{7} $ (or $ a \equiv 6 \pmod 7, b \equiv 1 \pmod 7 $ can work. This yields $ (a, b) = (43, 13) $ or $ (13, 43) $.