1) Find all prime numbers that divide 50!

2) If p and are both prime numbers, prove that is also prime.

3) (a) If p is a prime, and , prove that in the AP a, , , , , every pth term is divisible by p.

3) (b) From part a, conclude that if b is an odd integer, then every other term in the indicated progression is even.

4) Let denote the nth prime. For , show that .

Hint: Use induction and Bertrand's conjecture.

5) Prove that for every , there exists a prime p with .

More later,

Regards,

Nalin Pithwa

### Like this:

Like Loading...

*Related*