Question

prove that if p is. prime number and it divides a^2 then it divides a

Answer 1

Given p is a prime number .

p divides a² .

p | a²

Let p = a² k , k is an integer .

⇒ p = a²k

⇒ k = a²/p

⇒ k = ( a × a ) / p

If p | ab then p | a and p | b also  .

This means p | a

Hence proved.