Question

证明:3的n+2次方-2的n+2次方+3的n次方-2的n次方能被10整除

Answer 1

3的n+2次方-2的孝含n+2次方+3的n次方-2的n次方
=3^n(3^2+1)-2^n(2^2+1)
=3^n×10-2^n×5
=3^n×10-2^（迹键n-1）×10
=[3^n-2^(n-1)]×10
能姿慎巧被10整除