what is the remainder when you divide 2^203+5^300*7^100 by 7?

Question

i think..the answer is 2..can someone confirm for me

Answer 1

First of all, we can ignore the last term since it is a
multiple of 7. So we need the remainder of 2^203
when divided by 7.
But 2^1 = 2(mod 7)
2^2 = 4(mod 7)
2^3 =1( mod 7)
So the cycle of remainders repeats every 3 powers.
So 2^203 = (2^67)^3 *2^2 = 4(mod 7).
The remainder is 4.

Answer 2

4

Answer 3

too many numbers too fit in calculator. Try an online calculator