(12)

Using the binomial expansion in 7 103 = (7 2 ) 51 . 7 = (51 - 2) 51 . 7 we get,

(51 - 2) 51 . 7 = 7.( 51 C 0 51 51 .2° - 51 C 1 51 50 .2 1 +.......- 51 C 51 2 51 )

Now 51 is divisible by 17, so when above equation is divided by 17 we get, 7.(-2 51 ) as remainder,

Now again using binomial in 7.(-2 51 )= -56(2 4 ) 12 = -56(17 - 1) 12 we get,

-56(17 - 1) 12 = -56( 12 C 0 17 12 -1° - 12 C 1 l7 11 . 1 1 +.......+ 12 C 12 1 12 )

Now dividing above equation by 17 we get, (-56 x 1) 17= -5,

Now changing negative remainder to positive we get, -5 + 17 = 12,

Hence, when 7 103 divided by 17 gives 12 as remainder

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