If m and n are positive integers more than or equal to 2, `mgtn`, then (mn)! is divisible by

If m and n are two integers such that m = n^(2) - n , then (m^(2) - 2m) is always divisible by

If m and n are positive integers and (m – n) is an even number, then (m^(2) - n^(2)) will be always divisible by

If (m)=64, where m and n are positive integers,find the value of n)^(mn)..

If m , n are positive integers and m+nsqrt(2)=sqrt(41+24sqrt(2)) , then (m+n) is equal to

If m and n are positive integers such that (m-n)^(2)=(4mn)/((m+n-1)) , then how many pairs (m, n) are possible?

Prove by induction that if n is a positive integer not divisible by 3. then 3^(2n)+3^(n)+1 is divisible by 13.

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

If n be a positive integer, then prove that 6^(2n)-35n-1 is divisible by 1225.