Question

求证:7|9^n+1-2^n+1

Answer 1

问：求证:7|9^n+1-2^n+1

答：求证:7|9^n+1-2^n+11+2^n=1+8^k 2^r=1+(1+7)^k 2^r7|1+2^n 即　7|1+2^r试遍r=0,1,2，上式都不成立，所以7不整除2^n+1,n为任意自然数