Determine if the congruence has solutions

[msimard8]

Homework Statement

Determine if the congruence has solutions. If it does, determine the complete solution

x^11 + 3x^10 + 5x ≡ 2 (mod 11)

Homework Equations

The Attempt at a Solution

i know that 11 | x^11 + 3x^10 + 5x -2

and where ax≡c (mod m) has a solutioon iff gcd(a,m) | c

and that's about it

i also know if x =1...then the gcd(11,9) | 2 ...meaning there is a solution

help

 

[Midy1420]

The only thing I can think about is checking each number 1-10 to see which has a remainder of 2.