Question

Determinati restul imparirii numarului n=$98^{98} - 26^{98}$ la 9

Answer 1

$Utilizam~identitatea:~(a+b)^n= M_{a}+b^n. \\ \\ 98^{98 }=(99-1)^{98}= ( 9*11-1) ^{98} = M_{9} +(-1)^{98}= M_{9} +1. \\ \\ -26^{98}=-(27-1)^{98}=-(9*3+1)^{98}= -(M_{9} +1)=- M_{9}-1 . \\ \\ 98^{98}-26^{98}= M_{9}+1- M_{9} -1= M_{9} \Rightarrow~\boxed{restul~este~0}.$

$M_{n}~inseamna~un~multiplu~al~numarului~natural~n.$