Integer Points on Hypersurfaces.
Integer points unusually close to elliptic curves.
Integer sequences and matrices over finite fields.
Integer sequences and periodic points.
Integer sequences avoiding prime pairwise sums.
Integer sequences, functions of slow increase, and the Bell numbers.
Integer sequences related to compositions without 2's.
Integer sets having the maximum number of distinct differences.
Integer solutions of a sequence of decomposable form inequalities
Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers.
Integer Valued polynomials over a number field.
Integers free of prime divisors from an interval, I
Integers free of prime divisors from an interval, II
Integers in number systems with positive and negative quadratic Pisot base
We consider numeration systems with base β and − β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z− β of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and u− β coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2 − mx − m, the languages coincide, while for other quadratic Pisot numbers the language...
Integers not of the form
Integers representable by .
Integers whose multiples have anomalous digital frequencies
Integers with a large friable component
Integers with a maximal number of Fibonacci representations
We study the properties of the function which determines the number of representations of an integer as a sum of distinct Fibonacci numbers . We determine the maximum and mean values of for .
Integers with a maximal number of Fibonacci representations
We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1.