Question

suma a trei numere naturale consecutive este 3^2020 care este ultima cifra a produsului

Answer 1

$\displaystyle\it\\fie~m\in\mathbb{N}~a.i.~(m-1)+m+(m+1)=3^{2020}.\\(m-1)+m+(m+1)=m-1+m+m+1=3m=3^{2020},~impartim~\\la~3~ambii~membri\implies \boxed{\it m=3^{2019}}.\\acum~incercam~sa~aflam~ultima~cifra~a~produsului~tinand~cont~ca\\3^{2019}=\mathcal{M}_{10}+7.\\atunci~avem~ca~produsul~U\bigg(\bigg(3^{2019}-1\bigg)3^{2019}\bigg(3^{2019}+1\bigg)\bigg)=\\U\bigg(3^{2019}-1\bigg)U\bigg(3^{2019}\bigg)U\bigg(3^{2019}+1\bigg)=\\\overline{...6}\cdot\overline{...7}\cdot\overline{...8}=\boxed{\overline{...6}}.$