GCD of truncated rows in Pascal's triangle.

Kaplan, Gil; Levy, Dan

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Gray-ordered binary necklaces.

Degni, Christopher, Drisko, Arthur A. (2007)

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On the solutions of $σ (n) = σ (n + k)$ .

Weingartner, Andreas (2011)

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On the irrationality of a divisor function series.

Friedlander, John B., Luca, Florian, Stoiciu, Mihai (2007)

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Partial sums of powers of prime factors.

De Koninck, Jean-Marie, Luca, Florian (2007)

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Ufnarovski, Victor, Åhlander, Bo (2003)

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Prime and composite terms in Sloane's sequence A056542.

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Square-free Lucas $d$ -pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Czechoslovak Mathematical Journal

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Let $d$ be a fixed positive integer. A Lucas $d$ -pseudoprime is a Lucas pseudoprime $N$ for which there exists a Lucas sequence $U (P, Q)$ such that the rank of $N$ in $U (P, Q)$ is exactly $(N - ε (N)) / d$ , where $ε$ is the signature of $U (P, Q)$ . We prove here that all but a finite number of Lucas $d$ -pseudoprimes are square free. We also prove that all but a finite number of Lucas $d$ -pseudoprimes are Carmichael-Lucas numbers.

Generalizations of Midy's theorem on repeating decimals.

Martin, Harold W. (2007)

Integers

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On the composition factors of a group with the same prime graph as $B_{n} (5)$

Azam Babai, Behrooz Khosravi (2012)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. The prime graph of $G$ is a graph whose vertex set is the set of prime divisors of $| G |$ and two distinct primes $p$ and $q$ are joined by an edge, whenever $G$ contains an element of order $p q$ . The prime graph of $G$ is denoted by $Γ (G)$ . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if $G$ is a finite group such that $Γ (G) = Γ (B_{n} (5))$ , where $n \geq 6$ , then $G$ has a unique nonabelian composition factor isomorphic to $B_{n} (5)$ or $C_{n} (5)$ .