On multiple sums of products of Lucas numbers.
On multiple twisted -adic -Euler -functions and -functions.
On multiple zeros of Bernoulli polynomials
On multiples of certain real sequences
On Multiples of Round and Pister Forms.
On multiplicative bases in abelian groups
On multiplicative magic squares.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively e-perfect numbers.
On multiplicatively perfect numbers.
On Mycielski's problem on systems of arithmetical progressions
On and .
On natural numbers having unique factorization in a quadratic number field, II
On n-derivations and Relations between Elements rⁿ-r for Some n
We find complete sets of generating relations between the elements [r] = rⁿ - r for and for n = 3. One of these relations is the n-derivation property [rs] = rⁿ[s] + s[r], r,s ∈ R.
On near-neighbor quadratic forms. (Autour des formes quadratiques quasi-voisines.)
On near-perfect and deficient-perfect numbers
For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
On near-perfect numbers
For a positive integer n, let σ(n) denote the sum of the positive divisors of n. We call n a near-perfect number if σ(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3⁴·7²·11²·19².
On new partition of numbers
On Newman's conjecture and prime trees.