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Question

What is the remainder when 7103 is divided by 50?


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Solution

7103=7×(49)51

= 7×(501)51

7×(501)51=7[51C0(50)5151C1(50)50+51C2(50)49............51C50(50)151C51]

7×(501)51=7[51C0(50)5151C1(50)50+51C2(50)49............51C50(50)11]

51C0(50)5151C1(50)50+51C2(50)49............51C50(50)1 is a multiple of 50.We will replace it with 50k

7×(501)51=7[50k1]

7×(501)51=7[50k149]+7×49 (we add and subtract 7 * 49)

7×(501)51=7[50k50]+343

7×(501)51=7[50k50]+300+43

The first two terms are multiple of 50.

The remainder will be 43.


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