If p is a prime greater than 3 then show that `2p+1 and 4p+1` cannot be primes simultaneously.

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

If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or b-=0 (mod p).

If p ge 5 is a prime number, show that p^2 + 2 is a composite number.

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

If 2^p + 1 is a prime number, then p must be power of:

If p is a prime number greater than 3, then (p^(2)-1) is always divisible by (a) 6 but not 12 (b) 12 but not 24(c)24 (d) None of these

Consider the following statements: 1. If p > 2 is a prime, then it can be written as 4n + 1 of 4n + 3 for suitable natural number n. 2. If p > 2 is a prime, then (p -1)(p +1) is always divisible by 4. Of these statements:

Prove that if p is a prime number greater than 2, then the difference [(2+sqrt(5))^p]-2^(p+1) is divisible by p, where [.] denotes greatest integer.

Prove that if p is a prime number greater than 2, then the difference [(2+sqrt(5))^p]-2^(p+1) is divisible by p, where [.] denotes greatest integer.