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 y2 ≡ x(x + 1) (x + r − 1)(modp) has a solution, we conjecture that r(p) ≤ r2 − r + 1 with equality for infinitely many primes p. A proof is sketched for r = 5. A further generalization to y2 ≡ (x + a1) (x + ar) is suggested, where the a's are fixed positive integers.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| ID Code: | 8610 |
| Deposited On: | 28 Oct 2010 11:19 |
| Last Modified: | 05 Dec 2011 03:58 |
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