AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the maximum and minimum values of the divisor function on intervals of length k
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractFor every positive integer N, we determine the maximum sizes of collections C and C' of divi...
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
Our objective is to provide an upper bound for the length ℓN of the longest run of consecutive integ...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractThis note is a sequel to an earlier paper of the same title that appeared in this journal. W...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractIn an article in Astérisque in 1979 Erdős conjectured the existence of a critical value α0∈(...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractFor every positive integer N, we determine the maximum sizes of collections C and C' of divi...
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
Our objective is to provide an upper bound for the length ℓN of the longest run of consecutive integ...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractThis note is a sequel to an earlier paper of the same title that appeared in this journal. W...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractIn an article in Astérisque in 1979 Erdős conjectured the existence of a critical value α0∈(...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractFor every positive integer N, we determine the maximum sizes of collections C and C' of divi...
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