`p` is a prime number and `n

p is a prime number and (2+3) s also a prime number.The number of numbers that p can assume 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

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 P_(1),P_(2),P_(3) are prime numbers and m,n, rare positive integers such that LCM(m,n,r)P_(1),P_(2)^(2)P_(3)^(3) and GCD(m,n,r)=P_(1)P_(2)P_(3) Then number of possible triplets of (m,n,r) are

If 25 -= 4 (mod p), where p is a prime number, then p is_________.

If 37 -= 18 (mod p), where p is a prime number then find p.

sqrtp (where p is a prime number) is