# HW 7 due Nov 2 2016

• Count the number of solutions to the equation $x^2 + 3 y^2 \equiv 1 \mod p$ in two-dimensional projective space working in the field with p elements, assuming p>3.  Use the procedure described in class to convert to a homogeneous polynomial to find the solutions at infinity.
• problem 10.2 of MNT
• problem 10.3 of MNT
• problem 10.7 of MNT
• compute the trace of every element of the field $F_2(t)$, where $t^2 + t + 1=0$.