Question

verify the theorem proved above for p = 2, p = 5 and for a square = 1, 4, 9, 25, 36, 49, 64 and 81.

Answer 1

Answer:

Step-by-step explanation:

Theorem : Let p be a prime number. If p divides a²  , (where a is a positive integer),  then p divides a

Let say prime factors of a are

a = p₁ , p₂ , p₃ ........., pₓ   where p₁ to pₓ are prime number

a = (p₁ × p₂ × p₃ ×.........× pₓ)

a² =  (p₁ × p₂ × p₃ ×.........× pₓ) (p₁ × p₂ × p₃ ×.........× pₓ)

if p divides a² then it is one of  (p₁ × p₂ × p₃ ×.........× pₓ)

as a = (p₁ × p₂ × p₃ ×.........× pₓ) so p divides a

Verification for

p = 2, p = 5 and for a square = 1, 4, 9, 25, 36, 49, 64 and 81.

2 is factor of 4 , 36 & 64

2 is factor of 2 , 6 & 8

5 is factor of 25

5 is a factor of 5 also

Answer 2

Answer:

1+1=2

ans don't know for me too