Let f(x)=x+2x^2+3x^3+4x^4+5x^5+6x^6 , and let S=[f(6)]^5+[f(10)]^3+[f(15)]^2. Compute the remainder when S is divided by 30.
Here's a hint on how to do the problem:
First, plug in the number 6 into f(6) and then use a similar technique to solve for f(10) and f(15) (Plug in 10 and 15 into f(x) to find f(10) and f(15)). Then, plug in the values of f(6), f(10), and f(15) into S and compute S. Lastly, divide S by 30 and you should get the answer.
Note: I believe that you can probably do this problem with a little help, so I'm not going to write down the answer.