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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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