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

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

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

For each positive integer n, let S_n =sum of all positive integers less than or equal on n. Then S_(51) equals

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

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

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