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[SOLVED] Simple algebra problem (fields)
Solve x²+x+41=0 in the fields Z43 and Z167
2. The attempt at a solution
Well Z43={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 Z167? I can't find any x that is in that field and solves the problem.
Homework Statement
Solve x²+x+41=0 in the fields Z43 and Z167
2. The attempt at a solution
Well Z43={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 Z167? I can't find any x that is in that field and solves the problem.