Question

What is the remainder when x^3 – 2x^2 + x + 1 is divided by (x -1)?

Answer 1

Answer:

I've put together the following congruences:

x = 8 (mod 13)

2x + 1234 = 7 (mod 17)

3x + 4321 = 6 (mod 19).

Using the formulas: x=x0+k(mgcd(a,m)), whereas ax0+my0=b. I've come to this:

x = 8 mod 13

x = 10 mod 17

x = 7 mod 19.

After that I've used Chinese Remainder theorem.

M1 = 323; x1 = 6; M2 = 247; x2 = 2; M3=221; x3 = 8.

I get 32820 mod 4199 = 3427 + 4199*k