Question

21.Find the remainder when 2⁸¹ is divided by 17.​

Answer 1

Answer:

Find the value of each of the following products

i) (-3) x 15Find the value of each of the following products

i) (-3) x 15

ii) 4 x (-13)

iii) (-23) x (-31)

iv) (-3) x (-2) x 7(-3) x (-2) x 7

Answer 2

Thus reminder is equal to 2 when 2^81 is divided by 17

Step-by-step explanation:

Solution:

We are going to using congruence relation to find the remainder

We know that

2^5 = 32

⇒ 2^5 = 15(mod 17)

Taking square on both sides we get

⇒ (2^5)² = 15²(mod 17)

⇒ 2^10 = 225(mod 17)

And 225 = 4(mod 17) So

⇒ 2^10 = 4(mod 17)

Taking square on both sides we get

⇒ (2^10)² = 4²(mod 17)

⇒ 2^20 = 16(mod 17)

Taking square on both sides we get

⇒ (2^20)² = (16)²(mod 17)

⇒ 2^40 = 256(mod 17)

And 256 = 1(mod 17) So

⇒ 2^40 = 1 (mod 17)

Taking square on both sides we get

⇒ (2^40)² = 1² (mod 17)

⇒ 2^80 = 1 (mod 17)

Multiplying by 2 on both sides we get

(2^80) × 2 = 1 × 2 (mod 17)

⇒ 2^81 = 2 (mod 17)

Thus reminder is equal to 2 when 2^81 is divided by 17