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《Journal of Anhui Normal University(Natural Science)》 2004-01
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SOME NECESSARY AND SUFFICIENT CONDITIONS ON LUCAS SEQUENCES

CHENG Rong-jun, ZHOU Fang-min(College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000)  
The lucas sequences U_n(u) and V_n(u) were defined as: U_0=0, V_0=2, U_1=1, V_1=u, U_n=uU_(n-1)-U_(n-2),V_n=uV_(n-1)-V_(n-2), n≥2. In this paper, we present some necessary and sufficient conditions on the systems of congruences: U_(N+r)(u)≡0 mod NV_(N+r)(u)2 mod NB),U_(N+r)(u)0 mod NV_(N+r)(u)≡2 mod N and U_(N+r)(u)0 mod NV_(N+r)(u)2 mod Nand estimate the number of u's satisfying the above systems respectively, where N=pq is a product of two odd primes, q=k(p+1)+r,|r|p+12,k≥7,(u~2-4p)=-1, and gcd(u,N)=gcd(u~2-4,N)=1.
【Fund】: 国家自然科学基金(10071001);; 安徽省自然科学基金(01046103);; 安徽省教育厅自然科学基金(2002KJ131)资助项目.
【CateGory Index】: O156
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【References】
Chinese Journal Full-text Database 2 Hits
1 ZHOU Fang-min,\ JI Yi-gui (College of Mathematics and Computer Sience, Anhui Normal University, Wuhu 241000, China);SOME PROPERTIES OF ONE PARAMETER QUADRATIC-BASE PSEUDOPRIMES[J];Journal of Anhui Normal University(Natural Science);2004-04
2 ZHOU Wei-ping1,2(1.College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China;2.College of Mathematics and ComputerScience,Anqing Normal College,Anqing 246011,China);A B_2(i≠j) Sequence with Larger Reciprocal Sum[J];Journal of Anhui Normal University(Natural Science);2006-04
【Co-references】
Chinese Journal Full-text Database 2 Hits
1 ZHOU Fang-min,\ JI Yi-gui (College of Mathematics and Computer Sience, Anhui Normal University, Wuhu 241000, China);SOME PROPERTIES OF ONE PARAMETER QUADRATIC-BASE PSEUDOPRIMES[J];Journal of Anhui Normal University(Natural Science);2004-04
2 Zhang Zhen-xiang State Key Laboratory of Information Security, and Anhui Normal University;ON THE COMPLEXITY OF AN ALGORITHM FOR INTEGER VECTOR CONVELUTIONS[J];Mathematica Numerica Sinica;1993-01
【Secondary References】
Chinese Journal Full-text Database 4 Hits
1 JI Yi-gui(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Finding Carmicheal Numbers Which Are Also Strong Pseudoprimes[J];Journal of Anhui Normal University(Natural Science);2006-02
2 ZHOU Wei-ping1,2(1.College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China;2.College of Mathematics and ComputerScience,Anqing Normal College,Anqing 246011,China);A B_2(i≠j) Sequence with Larger Reciprocal Sum[J];Journal of Anhui Normal University(Natural Science);2006-04
3 LIU Li (College of Mathematics and Computer Science,Anhui Normal University, Wuhu 241000,China);Notes on an Elliptic Curve Test for Mersenne Primes[J];Journal of Anhui Normal University(Natural Science);2007-01
4 ZHU Long(College of Mathematics and Computer Science,Anhui Normal University, Wuhu 241000,China);A Note on Problems of Euler Numbers[J];Journal of Anhui Normal University(Natural Science);2007-05
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