Question Number 143794 by Huy last updated on 18/Jun/21
$$\mathrm{Prove}\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{111}} +\mathrm{1}\vdots\mathrm{223} \\ $$
Commented by TheHoneyCat last updated on 18/Jun/21
$${sorry}\:{for}\:{my}\:{ignorance}; \\ $$$${what}\:{does}\:{a}\vdots{b}\:{means}? \\ $$$${I}'{ve}\:{notices}\:{it}\:{is}\:{defined}\:{on}\:{integers} \\ $$$${but}\:{I}'{ve}\:{never}\:{seen}\:{it}\:{elsewere} \\ $$$${and}\:{wikipedia}\:{says}\:{it}\:{is}\:{used}\:{to}\:{draw}\:{matixes}: \\ $$$$\begin{pmatrix}{\mathrm{1}}\\{\mathrm{2}}\\{\mathrm{3}}\\{\vdots}\\{{n}}\end{pmatrix} \\ $$
Commented by mr W last updated on 18/Jun/21
$${i}\:{think}\:{he}\:{means} \\ $$$$\mathrm{223}\:{divides}\:\mathrm{3}^{\mathrm{111}} +\mathrm{1},\:{i}.{e}. \\ $$$$\mathrm{3}^{\mathrm{111}} +\mathrm{1}\equiv\mathrm{0}\:{mod}\:\left(\mathrm{223}\right) \\ $$
Commented by TheHoneyCat last updated on 18/Jun/21
$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot} \\ $$