On Arithmetic Progressions of Equal Lengths

  • PRODUCTSby N . Saradha, T. N. Shorey, R . TijdemanAbstract
  • Published 1995

Abstract

It is shown that apart from (k + 1)(k + 2):::(2k) = 2 6:::(4k ? 2) for k = 2; 3; 4; ::: there are only nitely many arithmetic progressions with given diierences of equal lengths 2 and with equal products and that they can be eeectively determined. x1. Introduction. For positive integers d 1 ; d 2 and m 2, Saradha and Shorey studied the equation (1) in integers x > 0; y > 0 and k 2. In 5] and 6] they proved that equation (1) with d 1 = d 2 = d implies that max(x; y; k) is bounded by an eeectively computable number depending only on m and d. It was shown in 7] that equation (1) with m = 2 implies that either max(x; y; k) is bounded by an eeectively computable number depending only on d 1 and d 2 or k = 2; d 1 = 2d 2 2 ; x = y 2 + 3d 2 y. On the other hand, equation (1) with m = 2 is satissed whenever the latter possibility 1

Cite this paper

@inproceedings{Saradha1995OnAP, title={On Arithmetic Progressions of Equal Lengths}, author={PRODUCTSby N . Saradha and T. N. Shorey and R . TijdemanAbstract}, year={1995} }