On the number of large integer points on elliptic curves
On the number of lattice points in certain planar segments
On the number of lattice points inside a closed curve
On the number of m-term zero-sum subsequences
On the number of nonquadratic residues which are not primitive roots
We show that there exist infinitely many positive integers r not of the form (p-1)/2 - ϕ(p-1), thus providing an affirmative answer to a question of Neville Robbins.
On the number of orthogonal systems in vector spaces over finite fields.
On the number of pairs of binary forms with given degree and given resultant
On the number of pairs of partitions of n without common subsums
On the Number of Partitions of an Integer in the -bonacci Base
For each we consider the -bonacci numbers defined by for and for When these are the usual Fibonacci numbers. Every positive integer may be expressed as a sum of distinct -bonacci numbers in one or more different ways. Let be the number of partitions of as a sum of distinct -bonacci numbers. Using a theorem of Fine and Wilf, we obtain a formula for involving sums of binomial coefficients modulo In addition we show that this formula may be used to determine the number of partitions...
On the number of perfect binary quadratic forms.
On the number of places of convergence for Newton’s method over number fields
Let be a polynomial of degree at least 2 with coefficients in a number field , let be a sufficiently general element of , and let be a root of . We give precise conditions under which Newton iteration, started at the point , converges -adically to the root for infinitely many places of . As a corollary we show that if is irreducible over of degree at least 3, then Newton iteration converges -adically to any given root of for infinitely many places . We also conjecture that...
On the number of points on abelian and Jacobian varieties over finite fields
We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.
On the number of polynomials of bounded measure
On the number of prime divisors of a binomial coefficient.
On the number of prime divisors of the iterates of the Carmichael function.
On the number of prime divisors of the order of elliptic curves modulo p
On the number of prime factors of a finite arithmetical progression
On the number of prime factors of integers of the form ab + 1
On the number of prime factors of summands of partitions
We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.
On the Number of Primitive Lattice Points in Plane Domains.