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Answer 1

Answer:

Option(C)

Step-by-step explanation:

(21)

Given (15²³ + 19²³).

Here, a = 15, b = 19, n = 23{odd number}

We know that aⁿ + bⁿ is divisible by a + b{∴ n is odd}

Now,

a + b = 15 + 19

        = 34.

As 34 is a multiple of 17, 15²³ + 19²³ is divisible by 17.

So, Rem[(15²³ + 19²³)/17] = 0.

Hope it helps!

Answer 2

We know that : a ⁿ + b ⁿ is divisible by a + b if and only if n is odd!

[ Proof : https://brainly.in/question/6558444 ]

Given :

15 ²³ + 19 ²³ .

Comparing with aⁿ + bⁿ we get :

a = 15

b = 19

n = 23

n is odd.  So : a + b is divisible be  aⁿ + bⁿ

a + b = 15 + 19 = 34

aⁿ + bⁿ is divisible by 34 .

This means that  aⁿ + bⁿ is divisible by 17×2

So  aⁿ + bⁿ should be divisible by 17 as well as 2

Alas if  aⁿ + bⁿ is divided by 17 then I am afraid that the remainder is dead!

The remainder will be 0 as  aⁿ + bⁿ is divisible by 17 .

ANSWER :

$\boxed{\mathsf{OPTION\:\:C}}$

Hope it helps you ^_^

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