Question

求证:5的2次方乘以3的2n+1次方乘以2的n次方减去3的n次方乘以6的n+2次方能被13整除

Answer 1

5^2*3^(2n+1)*2^n-3^n*6^(n+2)

=25*3^(2n+1)*2^n-3^n*3^(n+2)*2^(n+2)

=25*3^(2n+1)*2^n-3^(2n+2)*2^(n+2)

=3^(2n+1)*2^n(25-3*2^2)

=13*3^(2n+1)*2^n

所以能被13整除