A recursive method to calculate the number of solutions of quadratic equations over finite fields

Author:
Kenichi Iyanaga

Journal:
Math. Comp. **64** (1995), 1319-1331

MSC:
Primary 11T30; Secondary 11D79, 11R29, 11Y16

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297472-6

MathSciNet review:
1297472

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Abstract | References | Similar Articles | Additional Information

Abstract: The number of solutions of the quadratic equation

*m*, with and belonging to a finite field, is studied and a recursive method to compute is established.

**[1]**T. Agoh,*A note on unit and class number of real quadratic fields*, Acta Math. Sinica (N.S.) 5 (1989), 281-288. MR**1019628 (90i:11124)****[2]**K. Ireland and M. Rosen,*A classical introduction to modern number theory*, Springer-Verlag, Berlin and New York, 1982. MR**661047 (83g:12001)****[3]**L. Maohua,*The number of solutions of a certain quadratic congruence related to the class number of*, Proc. Amer. Math. Soc.**117**(1993), 1-3. MR**1110547 (93c:11021)****[4]**Q. Sun,*On the number of solutions of**and the class number of*, Sichuan Daxue Xuebao**27**(1990), 260-264. MR**1077801 (91j:11002)****[5]**-,*On the number of solutions of*, Adv. in Math. (Beijing)**19**(1990), 501-502.**[6]**K. S. Williams,*The quadratic character of*, Math. Mag.**49**(1976), 89-90. MR**0392791 (52:13604)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297472-6

Keywords:
Quadratic equations over a finite field,
number of solutions,
algorithm

Article copyright:
© Copyright 1995
American Mathematical Society