Question

If p is a prime number and p divides (where k is a positive integer) then p must divide​

Answer 1

Answer:

then k is not a prime number

Answer 2

Given :  p is a prime number and p divides k²

To Find : then p must divide​

Solution:

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 divide  4.

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