Question

If $p_{1} and p_{2}$ are two odd prime numbers such that $p_{1} \ \textgreater \ p_{2}$, then $p^{2}_1 - p^{2}_2$ is
(a) an even number
(b) an odd number
(c) an odd prime number
(d) a prime number

Answer 1

SOLUTION :  

Option (a) is correct : AN EVEN NUMBER  

Given : p1 &  p2 are two odd prime numbers such that p1 > p2.

★★Let the two odd Prime numbers p1 = 5 & p2 = 3

Then , p1² = 5² = 25

p2² = 3² = 9

p1² - p2²  = 25 - 9 = 16 [EVEN NUMBER]

★★Let the two odd Prime numbers p1 = 7 & p2 = 5

Then , p1² = 7² = 49

p2² = 5² = 25

p1² - p2²  = 49 - 25 = 24 [EVEN NUMBER]

From the above 2 cases we can say that p1² - p2² is even number.

Hence, the correct option is (a)  AN EVEN NUMBER  

★★PRIME NUMBER : A number is called a prime number, if it has no factor other than one and the number itself.

E.g - 2, 3, 5, 7, 11, 23,.... are prime  numbers..

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

an even number - Option (a).

Step-by-step explanation:

Given that p₁ and p₂ are two odd prime numbers such that p₁ > p₂.

(i)

Let the two odd prime numbers be 7 and 5.

Here, p₁ = 7 and p₂ = 5. {p₁ > p₂}.

Now,

⇒ p₁² - p₂²

⇒ (7)² - (5)²

⇒ 49 - 25

⇒ 24.

Even number.

(ii)

Let the two odd prime numbers be 5 and 3.

Here, p₁ = 5 and p₂ = 3 {p₁ > p₂}

Now,

⇒ (p₁)² - (p₂)²

⇒ (5)² - (3)²

⇒ 25 - 9

⇒ 16.

Even number.

Therefore, p₁² - p₂² is an Even number.

Hope it helps!