p-adic valuations of some sums of multinomial coefficients
p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.
Palindromes in different bases: a conjecture of J. Ernest Wilkins.
Palindromic complexity of infinite words associated with non-simple Parry numbers
We study the palindromic complexity of infinite words , the fixed points of the substitution over a binary alphabet, , , with , which are canonically associated with quadratic non-simple Parry numbers .
Palindromic complexity of infinite words associated with non-simple Parry numbers
We study the palindromic complexity of infinite words uβ, the fixed points of the substitution over a binary alphabet, φ(0) = 0a1, φ(1) = 0b1, with a - 1 ≥ b ≥ 1, which are canonically associated with quadratic non-simple Parry numbers β.
Palindromic complexity of infinite words associated with simple Parry numbers
A simple Parry number is a real number such that the Rényi expansion of is finite, of the form . We study the palindromic structure of infinite aperiodic words that are the fixed point of a substitution associated with a simple Parry number . It is shown that the word contains infinitely many palindromes if and only if . Numbers satisfying this condition are the so-called confluent Pisot numbers. If then is an Arnoux-Rauzy word. We show that if is a confluent Pisot number then...
Palindromic squares for various number system bases
Parry expansions of polynomial sequences.
Partial sums of powers of prime factors.
Partitioning multipartite numbers into a fixed number of parts which satisfy congruence conditions.
Partitions in the prime number maze
Partitions quadratiques et cyclotomie
Pascal's triangle (mod 9)
Pattern occurrence in the dyadic expansion of square root of two and an analysis of pseudorandom number generators.
Pentagonal numbers in the Lucas sequence.
Perfect numbers and finite groups
Perfect powers with all equal digits but one.
Perfect, Semiperfect and Ore Numbers
Periodic expansions and units in quadratic and cubic number fields.
Periodic Jacobi-Perron expansions associated with a unit
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.