On a Theorem of S. Sivasankaranarayana Pillai
Let and a,q ∈ ℚ. Denote by the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve . We study the set and we parametrize it by the rational points of an algebraic curve.
Let be a monic polynomial which is a power of a polynomial of degree and having simple real roots. For given positive integers with and gcd with whenever , we show that the equationwith for has only finitely many solutions in integers and except in the case