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Results tagged with nt.number-theory
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user 4558
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
9
votes
1
answer
300
views
Composing two-term sums from the same primes
The following is an old result of Erdős and Turán (American Mathematical Monthly, 1934):
Given a set of $2^n + 1$ distinct positive integers, all of its two-term sums cannot be composed of the same $ …
- 7,857
4
votes
0
answers
263
views
What are the best bounds to date on the maximum girth of a cubic graph?
The girth of a graph is the length of its smallest cycle. Studying the maximum possible girth for a $k$-regular graph on $n$ vertices is a very well-studied problem.
In the 1988 paper "Ramanujan grap …
- 7,857
3
votes
Prime constellation conjectures
There is also a strengthening of Schinzel's hypothesis H known as the Bateman–Horn conjecture.
- 7,857
2
votes
2
answers
191
views
Ramanujan graphs from varieties over finite fields
Let $G$ be a $d$-regular graph. Let $d= \lambda_1 \ge \lambda_2 \ge \dots \ge \lambda_n \ge -d $ be the eigenvalues of the adjacency matrix of $G$, and set $\lambda = \max (|\lambda_2| , |\lambda_n|) …
- 7,857
0
votes
Ramanujan graphs from varieties over finite fields
Someone pointed me to a reference that answers my question about whether this example is new, so I will answer my own question in case it is helpful for anyone else.
This paper:
https://dl.acm.org/doi …
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