Question

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Verify the statement proved above for p=2, p=5 and for a2 = 1,4,9, 25, 36, 49,64
and 81
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Answer 1

Answer:

Step-by-step explanation:

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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