Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function $l^C_x$

• Autorzy: A. Rotkiewicz
• Języki publikacji: EN

Kategorie tematyczne

• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 91
• Numer: 1
• Strony: 75-83

Daty

wydano

1999

otrzymano

1998-05-26

poprawiono

1999-05-24

Twórcy

autor

A. Rotkiewicz

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

Bibliografia

• [1] W. R. Alford, A. Granville and C. Pomerance, There are infinitely many Carmichael numbers, Ann. of Math. (2) 140 (1994), 703-722.
• [2] N. G. W. H. Beeger, On even numbers m dividing $2^m - 2$, Amer. Math. Monthly 58 (1951), 553-555.
• [3] M. Cipolla, Sui numeri composti P, che verificano la congruenza di Fermat $a^{P-1} ≡ 1 (mod P)$, Ann. di Mat. (3) 9 (1904), 139-160.
• [4] J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, The primary pretenders, Acta Arith. 78 (1997), 307-313.
• [5] A. Korselt, Problème chinois, L'intermédiare des mathématiciens 6 (1899), 142-143.
• [6] C. Pomerance, A new lower bound for the pseudoprime counting function, Illinois J. Math. 26 (1982), 4-9.
• [7] C. Pomerance, I. L. Selfridge and S. S. Wagstaff, The pseudoprimes to 25·10⁹, Math. Comp. 35 (1980), 1003-1026.
• [8] P. Ribenboim, The New Book of Prime Number Records, Springer, New York, 1996.
• [9] A. Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of Faculty of Sciences, Univ. of Novi Sad, 1972.
• [10] A. Schinzel, Sur les nombres composés n qui divisent $a^n - a$, Rend. Circ. Mat. Palermo (2) 7 (1958), 37-41.
• [11] W. Sierpiński, A remark on composite numbers m which are factors of $a^m - a$, Wiadom. Mat. 4 (1961), 183-184 (in Polish; MR 23#A87).
• [12] W. Sierpiński, Elementary Theory of Numbers, Monografie Mat. 42, PWN, Warszawa, 1964 (2nd ed., North-Holland, Amsterdam, 1987).
• [13] K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. 3 (1892), 265-284.