Question

一道关于幂的数学题试说明:5^2*3^2n+1*2^n-3^n*6^n+2能被13整除^左边是底数,^右边是指数.*指的

Answer 1

证明：

5^2×3^(2n+1)×2^n-3^n×6^(n+2)

=5^2×3^(2n+1)×2^n-3^n×(2×3)^(n+2)

=5^2×3^(2n+1)×2^n-3^n×2^(n+2)×3^(n+2)

=5^2×3^(2n+1)×2^n-3^(2n+2)×2^(n+2)

=5^2×3^(2n+1)×2^n-3^(2n+1)×3×2^n×2^2

=3^(2n+1)×2^n×[5^2-3×2^2]

=3^(2n+1)×2^n×[25-12]

=3^(2n+1)×2^n×13

可以看出,上式是13的倍数,所以它能被13整除.