Question Number 22896 by jazary last updated on 23/Oct/17
![how can demonstred 17^(4n+1) +3×9^(2n+1) ≡0[11]](https://www.tinkutara.com/question/Q22896.png)
$${how}\:{can}\:{demonstred} \\ $$$$\mathrm{17}^{\mathrm{4}{n}+\mathrm{1}} +\mathrm{3}×\mathrm{9}^{\mathrm{2}{n}+\mathrm{1}} \equiv\mathrm{0}\left[\mathrm{11}\right] \\ $$
Commented by Rasheed.Sindhi last updated on 24/Oct/17
$$\mathrm{For}\:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{17}^{\mathrm{5}} +\mathrm{3}×\mathrm{9}^{\mathrm{3}} =\mathrm{1422044} \\ $$$$\mathrm{But}\:\mathrm{11}\:\nmid\:\mathrm{1422044} \\ $$$$\mathrm{Hence}\:\mathrm{the}\:\mathrm{given}\:\mathrm{congruence}\:\mathrm{is} \\ $$$$\mathrm{generally}\:\mathrm{false} \\ $$