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Question

What is the remainder when (13^{^{100}} + 17^{^{100}}) is divided by 25

CAT 2021

A
0
CORRECT ANSWER WRONG ANSWER
B
2
CORRECT ANSWER WRONG ANSWER
C
4
CORRECT ANSWER WRONG ANSWER
D
11
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(B)

Explanatory Answer :

we have to calculate this , (13^{100}+17^{^{100}})/ 25

As we know , Euler of 25 is 20

according to Euler

(a^{20})/ 25 = 1

Apply it here

 ((13^{20})^^{^{5}}+(17^{20})^^{^{5}})/ 25

=  (1^{5}+1^{5})/25

= 1+1/25

= 2/25

= 2 remainder

hence , B is the correct option