On the largest prime factors of n and n+1. (Short Communication).
On the least common multiple of Lucas subsequences
We compare the growth of the least common multiple of the numbers and , where is a Lucas sequence and is some sequence of positive integers.
On the least common multiple of -binomial coefficients.
On the least quadratic non-residue of a prime p ... 3 (mod 4).
On the length of continued fractions representing a rational number with given denominator
On the length of the continued fraction for values of quotients of power sums
Generalizing a result of Pourchet, we show that, if are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for tends to infinity as . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers , .
On the length of the period of ...d.
On the Lengths of the Periods of the Continued Fractions of Square-Roots of Integers.
On the logarithmic factor in error, term estimates in certain additive congruence problems
On the maximum row and column sum norm of GCD and related matrices.
On the Möbius function.
On the Möbius sum function
On the multiplicative order of modulo .
On the natural density of the range of the terminating nines function.
On the nonvanishing of Fermat quotients (mod p).
On the normality of arithmetical constants.
On the nth Powers of the Primitive Nth roots of Unity
On the number of binary signed digit representations of a given weight
Binary signed digit representations (BSDR’s) of integers have been studied since the 1950’s. Their study was originally motivated by multiplication and division algorithms for integers and later by arithmetics on elliptic curves. Our paper is motivated by differential cryptanalysis of hash functions. We give an upper bound for the number of BSDR’s of a given weight. Our result improves the upper bound on the number of BSDR’s with minimal weight stated by Grabner and Heuberger in On the number of...
On the number of distinct values of Euler's φ-function
On the number of elements with maximal order in the multiplicative group modulo n