A rational canonical form algorithm
We present an easy-to-implement algorithm for transforming a matrix to rational canonical form.
On fundamental solutions of binary quadratic form equations
We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation.
Extended GCD and Hermite normal form algorithms via lattice basis reduction.
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