Question Number 115932 by Khalmohmmad last updated on 29/Sep/20
$$\mathrm{13}^{\mathrm{14}} \boldsymbol{\div}\mathrm{4} \\ $$$$\mathrm{Remaining}? \\ $$
Answered by JDamian last updated on 29/Sep/20
$$\mathrm{13}^{\mathrm{14}} {mod}\:\mathrm{4}\:=\:\left(\mathrm{13}\:{mod}\:\mathrm{4}\right)^{\mathrm{14}} = \\ $$$$=\:\mathrm{1}^{\mathrm{14}} \:=\:\mathrm{1} \\ $$
Answered by Dwaipayan Shikari last updated on 29/Sep/20
$$\mathrm{13}\equiv\mathrm{1}\left(\mathrm{mod4}\right) \\ $$$$\mathrm{13}^{\mathrm{14}} \equiv\mathrm{1}\left(\mathrm{mod4}\right) \\ $$$$\mathrm{R}=\mathrm{1} \\ $$