Question Number 204717 by BaliramKumar last updated on 26/Feb/24
$$\frac{\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} \:+………+\:\mathrm{3}^{\mathrm{200}} }{\mathrm{13}}\:\overset{\mathrm{Remainder}} {=}\:? \\ $$
Answered by Rasheed.Sindhi last updated on 26/Feb/24
$$\mathrm{3}^{\mathrm{0}} +\mathrm{3}^{\mathrm{1}} +\mathrm{3}^{\mathrm{2}} +…+\mathrm{3}^{\mathrm{200}} \equiv\left(\mathrm{1}+\mathrm{3}+\mathrm{9}\right)×\mathrm{67}\left({mod}\:\mathrm{13}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\equiv\mathrm{13}×\mathrm{67}\equiv\mathrm{0}\left({mod}\:\mathrm{13}\right. \\ $$
Commented by BaliramKumar last updated on 26/Feb/24
$$\mathrm{thanks} \\ $$