Question

if p is a prime number and p divides k2, then p divides._______​

Answer 1

if p divides k2 then p divides k

Answer 2

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.

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