GATE | GATE-CS-2016 (Set 2) | Question 39

The value of the expression 1399(mod 17), in the range 0 to 16, is :

 
Note : This question was asked as Numerical Answer Type.
(A) 4
(B) 13
(C) 8
(D) 16


Answer: (A)

Explanation: We have 13 * 13 * 13 * … * 13 (total 99 terms)
 
By remainder theorem,
=> (-4) * (-4) * … * (-4) (total 99 terms)
=> 16 * 16 * … * 16 * (-4) (total 50 terms, 49 terms for 16 and one term for -4)
 
Reapplying remainder theorem,
=> (-1) * (-1) * … * (-1) * (-4) (total 50 terms, 49 terms for -1 and one term for -4)
=> (-1) * (-4)
=> 4
 
Thus, A is the correct option.

Quiz of this Question

My Personal Notes arrow_drop_up