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Facteurs premiers des coefficients binomiaux
Factorial ratios that are integers.
Factorisation de fractions rationnelles et de suites récurrentes
Factorisation de suites récurrentes linéaires
Factorisation de suites récurrentes linéaires et applications
Factorisation in fractional powers
Factors of a perfect square
We consider a conjecture of Erdős and Rosenfeld and a conjecture of Ruzsa when the number is a perfect square. In particular, we show that every perfect square n can have at most five divisors between and .
Factors of alternating sums of products of binomial and q-binomial coefficients
Factors of generalized Rudin-Shapiro sequences. (Facteurs des suites de Rudin-Shapiro généralisées.)
Factors of sums of powers of binomial coefficients
Falling factorials, generating functions, and conjoint ranking tables.
Fans and bundles in the graph of pairwise sums and products.
Farey fractions and sums over coprime pairs
Farey fractions with prime denominators
Farey series and the Riemann hypothesis
Farhi arithmetic functions associated to Lucas sequences
Fermat and Wilson quotients for -adic integers
Fermat -Fibonacci and -Lucas numbers
Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all -Fibonacci and -Lucas numbers which are Fermat numbers. Some more general results are given.
Fermat numbers and integers of the form