Solving for the 0's of a polynomial in a ring

[Werg22]

Say I have x^2 + 1 = 0 mod 7, it is clear that adding a linear polynomial congruent to 0 will give away the solution; problem is, what polynomial is that? Trial and error is quite tedious, though I doubt it, is there a direct way?

 

[matt grime]

I presume you mean that you're operating in the ring of integers mod 7. There are only 7 elements in that field. Finding the zeroes/roots should be trivial.

 

[Werg22]

I realized that 30 sec after I made that thread

 

[mathwonk]

some thinking seems in order before speaking, or asking. but with me asking often stimulates thought.