Find the remainder?

Question

Find the remainder when 27^37 + 9^37 + 3^37 + 1 is divided by 3^36 - 1.

^_^

Answer 1

I got 40 as follows:

Let a = 3^37. Then we want to divide a^3 + a^2 + a+ 1 by a/3 - 1. Just do a long division, treating a just as you would x in polynomial division. I got a quotient of 3 a^2 + 12 a +39 with a remainder of 40.

Answer 2

was this just a random question thrown out?

anyway, it's 6.082667877....... x 10^35. i hope that information was useful to you, somehow.