Question

Find the remainder when 397^3589+5 is divided by 398

Answer 1

Given : (397)³⁵⁸⁹ + 5 is divided by 398.

To Find : Remainder

(A)3

(B) 4

(C) 2

(D) 1​

Solution :

(397)³⁵⁸⁹ + 5 is divided by 398.

(397)³⁵⁸⁹ + 5

= (398 - 1 )³⁵⁸⁹ + 5

All terms of Expansion will have 398 except last term

= 398K  + (-1)³⁵⁸⁹  + 5

= 398K   -1  + 5

= 398K + 4

so remainder = 4

(397)³⁵⁸⁹ + 5 is divided by 398.  then remainder = 4

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