Darrell Cox

most citedCollatz Cycles and

3 n + c

Cycles

1 citations · 4 across the 5 of their papers we have counts for

collaborators

5 papers

math.GM2021★ 1 cited

Measuring Abundance with Abundancy Index

Kalpok Guha, Sourangshu Ghosh

A positive integer $n$ is called perfect if $σ (n) = 2 n$ , where $σ (n)$ denote the sum of divisors of $n$ . In this paper we study the ratio $\frac{σ ( n )}{n}$ . We define the function Ab…

math.NT2021★ 1 cited

The Farey Sequence and the Mertens Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Franel and Landau derived an arithmetic statement involving the Farey sequence that is equivalent to the Riemann hypothesis. Since there is a relationship between the Mertens funct…

math.GM2021★ 1 cited

Collatz Cycles and $3 n + c$ Cycles

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Halbeisen and Hungerbuhler determined optimal bounds for the length of rational Collatz cycles. Their methods are extended to $3 n + c$ cycles. Another sequence having properties simi…

math.GM2020★ 1 cited

Bounds of the Mertens Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function $lo g x! > ∣ M (x) ∣$ when $x > 1$ .…

math.GM2020

Sequences and Polynomial Congruence

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

In this paper, we shall find a new connection between $n$ th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discu…

Measuring Abundance with Abundancy Index

The Farey Sequence and the Mertens Function

Collatz Cycles and 3n+c Cycles

Bounds of the Mertens Function

Sequences and Polynomial Congruence

Collatz Cycles and $3 n + c$ Cycles