Counting certain quadratic partitions of zero modulo a prime number
Counting certain quadratic partitions of zero modulo a prime number
Abstract Consider an odd prime number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> <m:mo>≡</m:mo> <m:mn>2</m:mn> <m:mspace width="0.3em"/> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mrow> <m:mi>mod</m:mi> </m:mrow> <m:mspace width="0.3em"/> <m:mn>3</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3) . In this paper, the number of certain type of partitions of zero in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="double-struck">Z</m:mi> <m:mspace width="-0.1em"/> <m:mtext>/</m:mtext> <m:mspace …