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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.

The postage stamp problem and arithmetic in base $r$

Amitabha Tripathi (2008)

Czechoslovak Mathematical Journal

Let $h, k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $h A : = {a_{1} + a_{2} + \dots + a_{r} : a_{i} \in A, r \leq h}$ denote the set of all integers representable as a sum of no more than $h$ elements of $A$ , and let $n (h, A)$ denote the largest integer $n$ such that ${1, 2, ..., n} \subseteq h A$ . Let $n (h, k) : = {max}_{A} : n (h, A)$ , where the maximum is taken over all sets $A$ with $k$ elements. We determine $n (h, A)$ when the elements of $A$ are in geometric progression. In particular, this results in the evaluation of $n (h, 2)$ and yields surprisingly sharp lower bounds for $n (h, k)$ , particularly for $k = 3$ .

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The Pfaffian transform.

The phase transition of the number-theoretical spin chain.

The Picard group of Siegel modular threefolds.

The Piltz divisor problem in number fields: An improved lower bound by Soundararajan's method

The plank problem for symmetric bodies.

The Pólya-Vinogradov inequality for totally real algebraic number fields

The polylogarithm in the field of two irreducible quintics.

The polynomial part of a restricted partition function related to the Frobenius problem.

The polynomial $X^{2} + Y^{4}$ captures its primes.

The polynomial $x^{3} + x^{2} + x - 1$ and elliptic curves of conductor 11

The positivity problem for fourth order linear recurrence sequences is decidable

The postage stamp problem and arithmetic in base $r$

The power of a prime that divides a generalized binomial coefficient.

The power of powerful numbers.

The p-Primary Component of the Cuspidal Divisor Class Group on the Modular Curve X(p).

The primality of certain integers of the form $2 A r^{n} - 1$

The primary pretenders

The Prime Ideal Theorem in Non-Commutative Arithmetic.

The prime number theorem for Beurling's generalized numbers. New cases

The prime number theorem in short intervals for automorphic L-functions

Currently displaying 781 – 800 of 1340