R. Burns

activity

20162022

most citedStructure and asymptotics for Catalan numbers modulo primes using automata

3 citations · 13 across the 13 of their papers we have counts for

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Showing 2017 · math.NTShow all

4 papers · 2 filters

math.NT2017★ 1 cited

Representing numbers as the sum of squares and powers in the ring $Z_{n}$

Rob Burns

We examine the representation of numbers as the sum of two squares in $Z_{n}$ for a general positive integer $n$ . Using this information we make some comments about the dens…

math.NT2017

The Catalan numbers have no forbidden residue modulo primes

Rob Burns

Let $C_{n}$ be the $n$ th Catalan number. For any prime $p \geq 5$ we show that the set ${C_{n} : n \in N}$ contains all residues mod $p$ . In addition all residues are attai…

math.NT2017★ 1 cited

Structure and asymptotics for Motzkin numbers modulo primes using automata

Rob Burns

We establish a lower bound of 2/p(p-1) for the asymptotic density of the Motzkin numbers divisible by a general prime number p > 3. We provide a criteria for when this asymptotic d…

math.NT2017★ 3 cited

Structure and asymptotics for Catalan numbers modulo primes using automata

Rob Burns

Let $C_{n}$ be the $n$ th Catalan number. We show that the asymptotic density of the set ${n : C_{n} \equiv 0 mod p}$ is $1$ for all primes $p$ , We also show that if $n = p^{k} - 1$ the…

Representing numbers as the sum of squares and powers in the ring Zn​

The Catalan numbers have no forbidden residue modulo primes

Structure and asymptotics for Motzkin numbers modulo primes using automata

Structure and asymptotics for Catalan numbers modulo primes using automata

Representing numbers as the sum of squares and powers in the ring $Z_{n}$