Bui Minh Phong

On a Problem of Fabrykowski and Subbarao Concerning Quasi Multiplicative Functions Satisfying a Congruence Property

It follows from our result that if a quasi multiplicative function f satisfies the congruence f(n + p) ≡ f(n) (mod p) for all positive integers n and for all sufficiently large primes p, then there is a non-negative integer α such that f(n) = nα holds for all positive integers n. In particular, this gives an answer to the conjecture of Fabrykowski and Subbarao.

On generalized Lehmer sequences

where AB~O, D = A ~ 4 B ~ 0 and IGol+lGal~0. If G0=0 and GI=I , then we denote the sequence G(0, 1, .4, B) by R=R(.4, B). The sequence R is called Lucas sequence and R, is called a Lucas number. In 1930 D. H. Lehmer [2] generalized some results of Lucas on the divisibility properties of Lucas numbers to the terms of the sequence U=U(L, M)={U,}0 *~ which is defined by integer constants L, M, Uo=0, Ua= 1 and the recurrence

On Strong Normality

Abstract We introduce the concept of strong normality by defining strong normal numbers and provide various properties of these numbers, including the fact that almost all real numbers are strongly normal.

On the maximal exponent of the prime power divisor of integers

Abstract The largest exponent of the prime powers function is investigated on the set of numbers of form one plus squares of primes.

A Characterization ofnsas a Multiplicative Function

All those complex valued multiplicative functions f and g are characterized for which g(n + k) − f(n) → 0 (n → ∞) is satisfied (k is an arbitrary nonzero integer).