The positive integer k for which ((101)^(k/2))/k! is maximum is

The greatest positive integer k, for which 81^(k) + 1 is a factor of the sum 9^(350) + 9^(348) …… 9^(4) + 9^(2) + 1

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

The number of positive integers k for which the equation kx-12=3k has an integer solution for x is

The greatest +ve integer k, for which 4^k+1 is factor of sum 1+2+2^2+....+2^(99) is

What is the maximum value of n for which there is a set of distinct positive integers k_(2),...,k_(n), for which k_(1)^(2)+k_(2)^(2)+....+k_(n)^(2)=2002

For which positive integers n is the ratio (sum_(k=1)^(n)k^(2))/(sum_(k=1)^(n)k) an integer?

For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum_(k=1)^(n) k) an integer ?