TS ICET 2017 Question Paper with Solutions for online practice

Question : 109 of 200

Marks: +1, -0

For a positive integer k and integers a, b we write a ≡ b (mod k) if k divides a - b. If

5^2017

≡ m (mod 13) and 0 < m < 13, then m =

Solution:

On dividing 5n by 13, the remainders obtained are as under,

So, its cyclicity is 4.

2017=(4×504)+1

∴5^{2017}

on being divided by 13 leaves a remainder 5.

∴m=5

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