- #1
math-chick_41
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find a formula that depends on p
that determines the number of reducible monic degree 2 polynomials over Zp.
so the polynomials look like x^2+ax+b with a,b in Zp.
I examined the case for Z3 and Z5 to try and see what was going on.
in Z3 we had 9 monic degree 2 polynomials, 6 of them were reducible
and 3 were not. in Z5 we had 25 monic degree 2's 15 were reducible and
10 were not. it appears that (p(p+1))/2 is the formula but just showing two cases is obviously not enough work.
Is my guess right and how on Earth would I prove it.
thanks!
that determines the number of reducible monic degree 2 polynomials over Zp.
so the polynomials look like x^2+ax+b with a,b in Zp.
I examined the case for Z3 and Z5 to try and see what was going on.
in Z3 we had 9 monic degree 2 polynomials, 6 of them were reducible
and 3 were not. in Z5 we had 25 monic degree 2's 15 were reducible and
10 were not. it appears that (p(p+1))/2 is the formula but just showing two cases is obviously not enough work.
Is my guess right and how on Earth would I prove it.
thanks!
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