If n and p are positive integers such that `8(2^(p))=4^(n)`, what is n in terms of p?

If m and p are positive integer and (2sqrt(2))^(m)=32^(n) , what is the value of (p)/(m) ?

If n is a positive integer then .^(n)P_(n) =

If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the last digit of the expression will be -

If n be a positive integer and P(n):4^(5n)-5^(4n) P(n) is divisible by -

If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^(1//n) = 2 ( P^(2) + Q^(2))^(1//2n) cos (1/n , tan . Q/P) .

If (9+4sqrt(5))^(n)=p+beta , where n and p are positive integers and beta is a positive proper fraction, prrove that (1-beta)(p+beta)=1 and p is an odd integer.

If n ne 3p , and s = (n^(2)+p)/(n-3p) , what is the value of p in terms of n and s ?

If p is a fixed positive integer,prove by induction that p^(n+1)+(p+1)^(2n-1) is divisible by P^(2)+p+1 for all n in N

Let S_n denote the sum upto n terms of an AP . If S_n=n^2P and S_m=m^2P where m,n,p are positive integers and m ne n , then find S_p .