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Remainder: Part 2 (Posted on 2006-05-02) Difficulty: 2 of 5
What is the remainder when (19)^92 is divided by 92?

No Solution Yet Submitted by Ravi Raja    
Rating: 2.5000 (4 votes)

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Some Thoughts Solution | Comment 3 of 4 |

just keep on getting a smaller remainder.

19^92 mod 92


19^2=361 mod 92 =-7
so 19^92 = -7^46

-7^3=343 mod 92 = -25
=> -25^15 *-7
-25^2=625 mod 92 = 19
=> 19^7*25*7
19^2 mod 92 = -7

-7^3 mod 92 = -25

=>-25*19*25*7
=>-19*19*7
=> -7*-7

this gives 19^92 mod 92 = 49

  Posted by Vishal Gupta on 2006-05-02 14:45:39
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