Question

If p is a prime number and p divided K3, then p divides​

Answer 1

p is a prime number and p divides k³, then p divides. k also

Step-by-step explanation:

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

p  divides k³

=> k³  = pq  

as p is prime number

Hence q must have a factor of p² as well

so that cube can be formed

=>  k³  = p (p²s)

=> k³ = p³s

=> p³ divides k³

hence p divides k also

This is not true  if p is not prime

for example

8 divides 4³ = 64   but 8 can not divided 4.

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