Rational Points in Arithmetic Progression on the Unit Circle
13/4 A Clay Square
Lucknow - 226001
Department of Mathematics
Motilal Nehru National Institute of Technology
Allahabad - 211004
Several authors have considered the problem of finding rational points
i = 1, 2,..., n
on various curves f(x, y) = 0, including
conics, elliptic curves and hyperelliptic curves, such that the
x-coordinates xi, i = 1, 2,...,
n are in arithmetic progression. In
this paper we find infinitely many sets of three points, in parametric
terms, on the unit circle x2 + y2 = 1 such that the x-coordinates of
the three points are in arithmetic progression. It is an open problem
whether there exist four rational points on the unit circle such that
their x-coordinates are in arithmetic progression.
Full version: pdf,
Received December 10 2015; revised version received March 14 2016.
Published in Journal of Integer Sequences, April 7 2016.
Journal of Integer Sequences home page