Question

if p is a prime number and p divides K2 , then p divides _____​

Answer 1

p is a prime number and p divides k2, then p divides. k also

Step-by-step explanation:

p is a prime number hence p has only factor p & 1  

p  divides k²

=> k²  = pq  

as p is prime number

Hence q must have a factor of p as well

so that square can be formed

=>  k²  = p (ps)

=> k² = p²s

=> p² divides k²

hence p divides k also

This is not true for if p is not prime

for example

8 divides 4² = 16   but 8 can not divided 4.

Learn More:

p is a prime number and p divides k2, then p divides

https://brainly.in/question/23862355

find the truth value of all prime numbers are either even or odd ...

https://brainly.in/question/9141870

I am not a prime number one of my factor is 3 i am more than 8*8 i ...

https://brainly.in/question/14010699