Question Number 126269 by liberty last updated on 19/Dec/20
$${If}\:{n}\:{is}\:{an}\:{odd}\:{integer}\:,\:{show}\:{that}\:\mathrm{32} \\ $$$${divides}\:\left({n}^{\mathrm{2}} +\mathrm{3}\right)\left({n}^{\mathrm{3}} +\mathrm{7}\right)\:?\: \\ $$
Answered by MJS_new last updated on 19/Dec/20
$$\mathrm{not}\:\mathrm{true}\:\mathrm{for}\:{n}=\mathrm{3} \\ $$$$\mathrm{true}\:\mathrm{only}\:\mathrm{for}\:{n}=\mathrm{8}{k}+\mathrm{1} \\ $$
Commented by liberty last updated on 19/Dec/20
$${yes}….{right} \\ $$