If `P` is a prime, n is a positive integer and `n+p=2000, LCM` of `n and p` is `21879` then

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

If 'P' is a prime number such that p ge 23 and n+ p! + 1 , then the number of primes in the list n+ 1, n+2 , ….. , n+p-1 is

Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by ^E_p(n! ) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers The number of zeros at the end of 108! is

Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by E_p(n!) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers the exponent of 7 in ,^100c_50 is

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

Statement-I: The exponent of 3 in 100! is 48 . Statement-II: If n is a t ve integer and p is a prime number then exponent is [(n)/(p)]+[(n)/(p^(2))]+[(n)/(p^(3))]+...

If n be a positive integer and P_n denotes the product of the binomial coefficients in the expansion of (1 +x)^n , prove that (P_(n+1))/P_n=(n+1)^n/(n!) .

If p is a prime number,then LCM of p and (p+1) is

P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642, then the value of n is -

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