Chowla, P. ; Chowla, S.
(1976)
*On the integer points on some special hyper-elliptic curves over a finite field*
Journal of Number Theory, 8
(3).
pp. 280-281.
ISSN 0022-314X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002231...

Related URL: http://dx.doi.org/10.1016/0022-314X(76)90005-6

## Abstract

If _{r}(p) is the least positive integral value of x for which y^{2} ≡ x(x + 1) (x + r − 1)(modp) has a solution, we conjecture that _{r}(p) ≤ r^{2} − r + 1 with equality for infinitely many primes p. A proof is sketched for r = 5. A further generalization to y^{2} ≡ (x + a_{1}) (x + a_{r}) is suggested, where the a's are fixed positive integers.

Item Type: | Article |
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ID Code: | 8610 |

Deposited On: | 28 Oct 2010 11:19 |

Last Modified: | 05 Dec 2011 03:58 |

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