# Thread: Find all solutions, if any

1. ## Find all solutions, if any

Find all solutions, if any, to each of the following congruencies:

(x^2) -2 is congruent to 0(mod7)

(x^3)-2x+3 is congruent to 0(mod7)

I dont know if I am doing this right this is what I did
gcd(1,-2,7)=1
so there are 1*7 possible solutions
x= 0, 1, 2, 3, 4, 5, 6
solutions of x
-2 not congruent to 0(mod 7)
-1 not congruent to 0(mod 7)
7 congruent to 0(mod 7)
14 congruent to 0(mod 7)
23 not congruent to 0(mod 7)
34 not congruent to 0(mod 7)

so are the solutions 3 and 4 or am i doing it wrong.
I found the second congruency has no solution I hope!!!

2. Originally Posted by mandy123
Find all solutions, if any, to each of the following congruencies:

(x^2) -2 is congruent to 0(mod7)

(x^3)-2x+3 is congruent to 0(mod7)
Just check $x=0,1,2,3,4,5,6$.