I've been doing some work and I keep running into polynomials of the following form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] P(x,y,z) = ax^2 + by^2 + cz^2 + 2(exy + fxz + gyz) \mod p [/tex]

where [itex] a,b,c \in \mathbb{Z}_p/ \{0\} [/itex] and [itex] d , e, f \in \mathbb{Z}_p [/itex] . It would be great if I knew anything about the existence of roots of [itex] P [/itex], save for the trivial root [itex] x=y=z=0 [/itex] I've looked through some of my algebra books and number theory books, but didn't find anything that would help me answer this question.

Could anyone point me in the right direction? If anyone knows of a textbook that discusses this or theorem name, that'd be great. Thanks!

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# Roots of Polynomials modulo p

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