Topology of Numbers · Problem 4.3.2

Classification of Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · pells-equation

Problem

For the quadratic form x2−29y2x^2 - 29y^2 do the following things: (a) Draw the separator line and compute the continued fraction for 29\sqrt{29}. (b) Find the smallest positive integer solution of x2−29y2=−1x^2 - 29y^2 = -1. (c) Find a glide reflection symmetry of the separator line and use this to find the smallest positive integer solution of x2−29y2=1x^2 - 29y^2 = 1.

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