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**[SOLVED] Simple algebra problem (fields)**

**1. Homework Statement**

Solve x²+x+41=0 in the fields Z

_{43}and Z

_{167}

**2. The attempt at a solution**

Well Z

_{43}={0,1,...,42} so any y that is n=0 mod 43 works...

x²+x+41=0=43 -> x²+x=2 -> x=1

Is this how it's done or am I doing it incorrectly?

If the solution above is right, then what about the same equation in the field Z

_{167}? I can't find any x that is in that field and solves the problem.