JOHN C. SAUNDERS
YOU?
Author Swipe
View article: On Pell numbers representable as product of two generalized Fibonacci numbers
On Pell numbers representable as product of two generalized Fibonacci numbers Open
A generalization of the well-known Fibonacci sequence is the $k$-Fibonacci sequence with some fixed integer $k\ge 2$. The first $k$ terms of this sequence are $0,0, \ldots, 1$, and each term afterwards is the sum of the preceding $k$ terms…
View article: Density of sequences of the form $x_n=f(n)^n$ in $[0,1]$
Density of sequences of the form $x_n=f(n)^n$ in $[0,1]$ Open
In 2013, Strauch asked how various sequences of real numbers defined from trigonometric functions such as $x_n=(\cos n)^n$ distributed themselves $\pmod 1$. Strauch’s inquiry is motivated by several such distribution results. For instance,…
View article: Density of sequences of the form $x_n=f(n)^n$ in [0,1]
Density of sequences of the form $x_n=f(n)^n$ in [0,1] Open
In 2013, Strauch asked how various sequences of real numbers defined from trigonometric functions such as $x_n=(\cos n)^n$ distributed themselves$\pmod 1$. Strauch's inquiry is motivated by several such distribution results. For instance, …
View article: The number of k-tons in the coupon collector problem
The number of k-tons in the coupon collector problem Open
Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$ and that we keep …
View article: Generalised Fibonacci sequences constructed from balancing words
Generalised Fibonacci sequences constructed from balancing words Open
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference …
View article: Random Fibonacci sequences from balancing words
Random Fibonacci sequences from balancing words Open
We study growth rates of random Fibonacci sequences of a particular structure. A random Fibonacci sequence is an integer sequence starting with $1,1$ where the next term is determined to be either the sum or the difference of the two prece…
View article: A Model of Random Industrial SAT
A Model of Random Industrial SAT Open
One of the most studied models of SAT is random SAT. In this model, instances are composed from clauses chosen uniformly randomly and independently of each other. This model may be unsatisfactory in that it fails to describe various featur…
View article: Diophantine Equations Involving the Euler Totient Function
Diophantine Equations Involving the Euler Totient Function Open
We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci sequences.
View article: Problems in Combinatorial and Analytic Number Theory
Problems in Combinatorial and Analytic Number Theory Open
We focus on three problems in number theory.
\nThe first problem studies the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the n…
View article: MAHLER MEASURE OF ‘ALMOST’ RECIPROCAL POLYNOMIALS
MAHLER MEASURE OF ‘ALMOST’ RECIPROCAL POLYNOMIALS Open
We give a lower bound of the Mahler measure on a set of polynomials that are ‘almost’ reciprocal. Here ‘almost’ reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern may bre…
View article: Mahler Measure of "Almost" Reciprocal Polynomials
Mahler Measure of "Almost" Reciprocal Polynomials Open
Here we give a lower bound of the Mahler measure on a set of polynomials that are "almost" reciprocal. Here "almost" reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern br…
View article: On (a,b) Pairs in Random Fibonacci Sequences
On (a,b) Pairs in Random Fibonacci Sequences Open
We study the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number 1. We define the tree recursively in the following way: if…