In an earlier article (Parabola, 37(3), (2001), 7-11) I talked about computer algebra systems: software packages that, as the name suggests, do algebra.
The equation $x^2 - dy^2 = 1$, where $d$ is a given integer, is known as Pell’s equation.
PRIZEWINNERS – SENIOR DIVISION
Stewart Wilcox North Sydney Boys’ High School
Q1121. Prove that $g(x) = 30x3 + 80x2 + 72x + 66$ is irreducible over the integers by showing it has no roots modulo $13$. What are the roots of $g(x)$ modulo $7$?