What is the remainder when 45647^(1+4+9+...+625) is divided by 34?

Explanation:- 45647 when divided by 34 leaves a remainder of 19.and In the power we are getting square of nos 1+2^2+3^2......25^2 using sum formula we get this as 5525
so question reduces to 19^5525 divided by 34 we can further apply euler no concept to find that 16th power will give remainder of 1 so question becomes
(19^5)/34 gives rem 15

sry cal mistake

when u first divide 45647 with 34 remainder is 19

19^9=171 & 34x5=170

the exponent of 45647 is 25x13x17

so the remainder of (25x13x17) with 9 will be 8

so remaining will be 19^8/34

so remainder will be 15

No guys ans is 15 please provide solution

1

u don't know....