Pentagonal numbers in the Lucas sequence.

Luo, Ming

Displaying similar documents to “Pentagonal numbers in the Lucas sequence.”

Fibonacci and Lucas numbers with only one distinct digit.

Luca, F. (2000)

Portugaliae Mathematica

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Tribonacci modulo $p^{t}$

Jiří Klaška (2008)

Mathematica Bohemica

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Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus $p$ and by its powers $p^{t}$ , which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.

On the basic character of residue classes.

Peter J. Hilton, Jennifer Hooper, Jean Pedersen (1989)

Publicacions Matemàtiques

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Let t, b be mutually prime positive integers. We say that the residue class t mod b is basic if there exists n such that t ≡ -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy p ≡ 3 mod 4, then t is basic mod b if t is a quadratic non-residue mod p for all such p; and t is not basic mod b if t is a quadratic residue mod p for all such p. If, for all...