Question

According to the fundamental theorem of arith-metic, if T (a prime

number) divides b2, b > 0, then​

Answer 1

Answer:

Let b=p

1

​

.p

2

​

.p

3

​

.p

4

​

.....p

n

​

where p

1

​

,p

2

​

,p

3

​

,.. are prime numbers which are necessarily not distinct,

⇒b

2

=(p

1

​

.p

2

​

.p

3

​

.p

4

​

.....p

n

​

)(p

1

​

.p

2

​

.p

3

​

.p

4

​

.....p

n

​

)

It is given that p divides b

2

.

From Fundamental theorem of Arithmetic, we know that every composite number can be expressed as product of unique prime numbers.

This means p belongs to p

1

​

,p

2

​

,p

3

​

,..p

n

​

and is one of them.

Also, b=p

1

​

.p

2

​

.p

3

​

.p

4

​

...p

n

​

, thus p divides b.

Step-by-step explanation:

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Answer 2

Answer:

answer is p divides b

Step-by-step explanation:

when t decides b2 then t decided b