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I am trying to solve the following:

99^7 (mod 123) = 54
Applying formula:
=(99 * 99^2 * 99^4) (mod 123)
= [(99 mod 123) * (99 ^2 mod 123)  * (99^4 mod 123)] mod 123
= [24* 75 * 75 * 75] mod 123 = 10,125,000 mod 123 = 82,317 * 123 
=10,124,991=9

With out using the formula, I am getting 54 but if I use formula, then I get 9.

Somebody please guide me.

Zulfi.

zak100
  • 177

1 Answers1

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Your working is incorrect. The answer is indeed 54.

Hint: What is $99^2 \pmod{123}$?

Calvin Lin
  • 68,864
  • I got it: [(99 mod 123) * (99 ^2 mod 123) * (99^4 mod 123)] mod 123 = [(24) * (9801 mod 123) (99^4 mod 123)] mod 123 = [[24 * 84 * 84 * 84] mod 123] mod 123 = 69 mod 123 = 54. Thanks a lot. God bless you. – zak100 Dec 04 '19 at 16:55