Question

aratati ca numarul A=9²⁰⁰⁶-7²⁰¹² se divide cu 10​

Answer 1

$\displaystyle\it\\A=9^{2006}-7^{2012}=(10-1)^{2006}-(10-3)^{2012}=\\\mathcal{M}_{10}+1-\mathcal{M}_{10}-3^{2012},~cunoastem~ca~3^{4k}=\mathcal{M}_{10}+1 \implies\\A=\mathcal{M}_{10}+1-1=\mathcal{M}_{10},~ca~atare,~10|A.$