Question

11•j=1(mod 4). Find j

Answer 1

Let us solve $11\cdot j=1(\mod 4).$ This congruence is equivalent to $(11-12)\cdot j=1(\mod 4),$ and hence $- j=1(\mod 4).$ We conclude that $j=-1(\mod 4)=3(\mod 4).$ Therefore, $j=3+4t,$ where $t\in \Z.$