Question

Hey guys hlp me with this qstn!!!

Answer 1

Answer:

(a) a is a positive integer.

is the answer.

Step-by-step explanation:

Let a=p1.p2.p3.p4.p5.....pn where, p1, p2, p3, ..., pn are prime numbers, which are necessarily not distinct.

⇒a^2=(p1.p2.p3.p4.p5.....pn).(p1.p2.p3.p4.p5......pn)

It is given that p divides a^2.

From the Fundamental theorem of Arithmetic,

we know that every composite number can be expressed as product of unique prime numbers.

This means that p is one of the numbers from (p1.p2.p3.p4.p5......pn).

We have a=(p1.p2.p3.p4.p5..pn) and p is one of the numbers from (p1.p2.p3.p4.p5......pn).

It means that p also divides a.

Hence, it is proved that if p divides a^2 then it also divides a.