请教初一的数学题急求证：N=52*32n+1*2n－3n*3n*6n+2能被13整除．2 2n+1 n n n n+2分别是5 3 2 3 3 6的乘方.哪位朋友能列举解题步骤?谢谢!
2019-04-13
请教初一的数学题
急求证：N=52*32n+1*2n－3n*3n*6n+2能被13整除．
2 2n+1 n n n n+2分别是5 3 2 3 3 6的乘方.哪位朋友能列举解题步骤?谢谢!
优质解答
是不是求证这个多项式能被13整除?
N=(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^n*2^n*2^2*3^n+1*3
=5^2*(3^2n+1*2^n)-(3^2n+1*2n)*2^2*3
=(25-12)*(3^2n+1*2^n)
=13*(3^2n+1*2^n)
我刚才就在做这道题……
是不是求证这个多项式能被13整除?
N=(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^n*2^n*2^2*3^n+1*3
=5^2*(3^2n+1*2^n)-(3^2n+1*2n)*2^2*3
=(25-12)*(3^2n+1*2^n)
=13*(3^2n+1*2^n)
我刚才就在做这道题……