Question

What is the remainder when 6^17 + 117^17 is divided by 7?

Answer 1

Step-by-step explanation:

6/7 remainder = 6

6^2/7 = 36/7 remainder = 1

6^3/7 = 216/7 remainder = 6

similarly 6^17/7 remainder = 6

comes to 117^6 in number theory there is fermat's theorem

a^(p-1) = 1mod p here p = 7 a 117 so remainder will be 1

now above problem can be written as 6^17/7 + 117^6/7

or remainder 6/7+1/7

or 7/7

so 0 will be the remainder