Math, asked by tarakapappu485, 10 months ago

The value of 147^23(mod 153) is

Answers

Answered by AditiHegde
2

Given:

147^23(mod 153)

To find:

The value of 147^23(mod 153) is

Solution:

From given, we have a power mod,

147^23 (mod 153)

with, base = 147

exponent = 23

The given, power mod is in form of a^b (mod n)

Steps to solve:

Divide the exponent b into the powers of 2 by writing it in binary.

So, we have, b = 23 = 10111

(23)₂ = 10111

      c₀ = 1

1       c₁ = 1² × 147¹ = 294 ≡ 141 mod 153

0      c₂ = 141² × 147⁰ = 282 ≡ 129 mod 153

1       c₃ = 129² × 147¹ = 37926 ≡ 135 mod 153

1       c₄ = 135² × 147¹ = 39690 ≡ 63 mod 153

1       c₅ = 63² × 147¹ = 18522 ≡ 9 mod 153

∴ 147^23 ≡ 54 mod 153

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