The value of 147^23(mod 153) is
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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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