Displaying similar documents to “GCD of truncated rows in Pascal's triangle.”

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.

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 ≥ 6 , then G has a unique nonabelian composition factor isomorphic to B n ( 5 ) or C n ( 5 ) .