平方剰余の相互法則
{\displaystyle {\begin{aligned}5&=1^{2}+2^{2},&113&=7^{2}+8^{2},&277&=9^{2}+14^{2},&421&=14^{2}+15^{2},\\13&=2^{2}+3^{2},&137&=4^{2}+11^{2},&281&=5^{2}+16^{2},&433&=12^{2}+17^{2},\\17&=1^{2}+4^{2},&149&=7^{2}+10^{2},&293&=2^{2}+17^{2},&449&=7^{2}+20^{2},\\29&=2^{2}+5^{2},&157&=6^{2}+11^{2},&313&=12^{2}+13^{2},&457&=4^{2}+21^{2},\\37&=1^{2}+6^{2},&173&=2^{2}+13^{2},&317&=11^{2}+14^{2},&461&=10^{2}+19^{2},\\41&=4^{2}+5^{2},&181&=9^{2}+10^{2},&337&=9^{2}+16^{2},&509&=5^{2}+22^{2},\\53&=2^{2}+7^{2},&193&=7^{2}+12^{2},&349&=5^{2}+18^{2},&521&=11^{2}+20^{2},\\61&=5^{2}+6^{2},&197&=1^{2}+14^{2},&353&=8^{2}+17^{2},&541&=10^{2}+21^{2},\\73&=3^{2}+8^{2},&229&=2^{2}+15^{2},&373&=7^{2}+18^{2},&557&=14^{2}+19^{2},\\89&=5^{2}+8^{2},&233&=8^{2}+13^{2},&389&=10^{2}+17^{2},&569&=13^{2}+20^{2},\\97&=4^{2}+9^{2},&241&=4^{2}+15^{2},&397&=6^{2}+19^{2},&577&=1^{2}+24^{2},\\101&=1^{2}+10^{2},&257&=1^{2}+16^{2},&401&=1^{2}+20^{2},&593&=8^{2}+23^{2},\\109&=3^{2}+10^{2},&269&=10^{2}+13^{2},&409&=3^{2}+20^{2},&601&=5^{2}+24^{2}.\end{aligned}}}