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Can the coefficients of these two pairs of polynomials be reduced? If yes, how do you do it with sagemath?

asked 2022-09-26 16:53:48 +0100

Periodic_1_6 gravatar image

updated 2022-09-27 11:00:15 +0100

Can the coefficients of these two pairs of polynomials be reduced?

If yes, how do you do it with sagemath?

(8223*b+6341)*(8221*a+6339) mod 67586227 = 0

(8213-8*b)*(8215-8*a) = 67586227

or

(8223*b+6341)*(8215-8*a) mod 67586227 = 0

(8221*a+6339)*(8213-8*b) mod 67586227 = 0
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answered 2022-09-27 00:07:29 +0100

One option is to work with polynomials, say with integer coefficients:

sage: S.<a,b> = ZZ[]
sage: f = (8223*b+6341)*(8221*a+6339)

Now reduce f mod 67586227:

sage: R = IntegerModRing(67586227)
sage: f
67601283*a*b + 52129361*a + 52125597*b + 40195599
sage: f.change_ring(R)
15056*a*b + 52129361*a + 52125597*b + 40195599
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@John Palmieri there were errors, now it is corrected excuse me

Periodic_1_6 gravatar imagePeriodic_1_6 ( 2022-09-27 11:02:06 +0100 )edit

I showed how to reduce the first one; you can do the same with all of the others.

John Palmieri gravatar imageJohn Palmieri ( 2022-09-27 16:41:36 +0100 )edit

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Asked: 2022-09-26 16:53:48 +0100

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Last updated: Sep 27