|Nov17-12, 04:37 PM||#1|
Modular arithmetic with a variable modulus and fractions
(This is my first post.)
I can't seem to find a good way of solving this sort of congruence for x:
x^2 / 3 + 11 [itex]\equiv[/itex] 5 (mod x)
Through trial and error it appears at least 3 and 6 are answers, but how can you reach them regularly? (I'm heard conflicting things about fractions being defined for modular arithmetic. It might be that this isn't even a createable congruence.)
|Nov17-12, 11:11 PM||#2|
1/3 (6) does not exist because there is no number x s.t. 3x[itex]\equiv[/itex]1 (6).
6/15 (9) is ok because HCF(15,9) = 3, which cancels to produce 2/5 (9) = 4.
|fractions, modular arithmetic, variable modulus|
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