求证N=5^2*2^2n+1*2^n-3^n*3^n*6^n+1能被13整除
问题描述：
求证N=5^2*2^2n+1*2^n-3^n*3^n*6^n+1能被13整除
答
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 =...