`Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n)

Prove that (n !)! is divisible by (n !)^((n-1)!)

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 a, b, c in N , the probability that a^(2)+b^(2)+c^(2) is divisible by 7 is (m)/(n) where m, n are relatively prime natural numbers, then m + n is equal to :

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 I_(m,n)= int(sinx)^(m)(cosx)^(n) dx then prove that I_(m,n) = ((sinx)^(m+1)(cosx)^(n-1))/(m+n) +(n-1)/(m+n). I_(m,n-2)

If the least common multiple of m and n is 24, then what is the first integer larger than 3070 that is divisible by both m and n?

Prove that n^2-n divisible by 2 for every positive integer n.

Let A=Z , the set of integers. Let R_(1)={(m,n)epsilonZxxZ:(m+4n) is divisible by 5 in Z} . Let R_(2)={(m,n)epsilonZxxZ:(m+9n) is divisible by 5 in Z} . Which one of the following is correct?

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

In the expansion of (1+a)^(m+n) ,prove that coefficients of a^(m) and a^(n) are equal.