Question

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

CAT 2021

A
B
C
D
##### 11
Solution

Correct option is

(B)

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