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Calculus and Beyond Homework Help
Finding inverse in polynomial factor ring
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[QUOTE="PsychonautQQ, post: 4996589, member: 482086"] [h2]Homework Statement [/h2] find the inverse of r in R = F[x]/<h>. r = 1 + t - t^2 F = Z_7 (integers modulo 7), h = x^3 + x^2 -1 [h2]Homework Equations[/h2] None [h2]The Attempt at a Solution[/h2] The polynomial on bottom is of degree 3, so R will look like: R = {a + bt + ct^2 | a,b,c are elements of z_7 and x^3 = 1 - ^2} To solve this problem I realized that the inverse must obviously have the form of some element in R, so I set up: (a + bt + ct^2)(1 + t - t^2) = 1 then I multiplied it all out whilst continuously substituting for t^3 and then solving for coefficients where the constant coefficient should equal 1 and the other two should equal 0. I did all of this and got the constant coefficient to be zero and nonzero answers for the other two >.<. I checked my calculations and can't find an error (doesn't necessarily mean there isn't one...), is something wrong with the way I set up the problem? is my substitution for x^3 correct? [/QUOTE]
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Finding inverse in polynomial factor ring
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