The largest integer `n` for which `n+5` divides `n^5+5` is:

The largest integer n for which 34! Is divisible by 3^n is

The largest integer n for which 34! Is divisible by 3^n is

The largest value of the positive integer k for which n^(k)+1 divides 1+n+n^(2)+ . . . .+n^(127) , is

The largest value of the positive integer k for which n^(k)+1 divides 1+n+n^(2)+ . . . .+n^(127) , is

Let n ( gt 1 ) be a positive integer, the largest integer m such that ( n ^(m) + 1) divides : ( 1+ n + n^(2) + "………" n^(127)) is :

Let f(n)=10^n+3 . 4^(n+2)+5, n in N . The greatest integer which divides f(n) for all n is

The least positive integer n such that 2 divides n,3 divides n+1,4 divides n+2,5 divides n+3 and 6 divides n+4 is

If m and n are any two odd positive integers with n