A number theory problem by Srinidhi U.S

Find the remainder when 2222^5555 is divided by 7 ?


The answer is 5.

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1 solution

Srinidhi U.S
Aug 30, 2015

2222 = 3 mod 7

                2222^3 = 3^3 mod 7

                                   = 6 mod 7

                                   = -1 mod 7

[(2222)^3]^1851=(-1)^1851 mod 7

        2222^5553 = (-1) mod 7                                       .....(1)

                                 and

                 2222^2 = 2 mod 7                                           .......(2)

from (1) and (2) we get,

                                               2222^5555 = (-2) mod 7

               therefore, the remainder is  5

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