On Lucas pseudoprimes with a prescribed value of the Jacobi symbol

• Autorzy: Rotkiewicz, A. , Schinzel, A.
• Języki publikacji: EN

Abstrakty

EN

Given integers P, Q with D = P^2 - 4Q [is not equal to] 0, -Q, -2Q, -3Q and [epsilon] = [...]1 every arithmetic progression ax + b, where (a, b) = 1 which contains an odd integer n[sub 0] with (D/n[sub 0]) = [epsilon] contains infinitely many strong Lucas pseudoprimes n with parameters P and Q such that (D/n) = [epsilon]. This theorem gives an affirmative answer to a question of C. Pomerance.

Słowa kluczowe

PL

ciąg Lucasa; teoria liczb

EN

Lucas pseudoprime; Lucas sequences; pseudoprime; strong Lucas pseudoprime

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 1
• Strony: 77--80
• Opis fizyczny: Bibliogr. 7 poz.,

Twórcy

autor

Rotkiewicz, A.

• Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland,

autor

Schinzel, A.

• Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland,

Bibliografia

• [1] R. Baillie, S. Wagstaff Jr., Lucas pseudoprimes, Math. Comp., 35 (1980) 1391-1417.
• [2] H. J. A. Duparc, On almost primes of the second order, Math. Centrum Amsterdam, Rap. ZW 1955-013, (1955) 1-13.
• [3] P. Erdös, P. Kiss, A. Sirközy, Lower bound for the counting function of Lucas pseudoprimes, Math. Comp., 51 (1988) 315-323.
• [4] J. F. Grantham, Frobenius pseudoprimes, A dissertation submitted to the Graduate Faculty of the University of Georgia, Athens, GA, 1997.
• [5] E. Lehmer, On the infinitude of Fibonacci pseudoprimes, Fibonacci Quart., 2 (1964) 229-230.
• [6] B. M. Phong, On the distribution of Lucas and Lehmer pseudoprimes, Ann. Univ. Sci. Budapest, Sect. Comp., 14 (1994) 145-163.
• [7] A. Rotkiewicz, On strong pseudoprimes in the case of negative discriminant in arithmetic progressions, Acta Arith., 68 (1994) 145-151.