\(\text{Giải}\)
\(5^{70}+7^{50}=25^{35}+49^{25}\)
\(25\equiv1\left(\text{mod 12}\right);49\equiv1\left(\text{mod 12}\right)\)
\(\Rightarrow5^{70}+7^{50}\equiv\left(1+1\right)\left(\text{mod 12}\right)\equiv2\left(\text{mod 12}\right)\)
\(\Rightarrow\text{5^70+7^50 chia 12 dư 2}\)
ta có : \(5^2\equiv1\)( mod 12 ) \(\Rightarrow\left(5^2\right)^{35}\equiv1\)( mod 12 )
hay \(5^{70}\equiv1\)( mod 12 ) (1)
\(\Rightarrow\left(7^2\right)\equiv1\)( mod 12 ) \(\Rightarrow\left(7^2\right)^{25}\equiv1\)( mod 12 ) hay \(7^{50}\equiv1\)( mod 12 ) ( 2 )
từ ( 1 ) ; ( 2 ) suy ra \(5^{70}+7^{50}\div12\) dư 2
mik ko copy ,tại mik đánh chậm thôi. hơn nữa bài ko giống nhau cũng đc gọi là cpy á ?
