(Preamble: This post is an offshoot of this MSE question, and the answers contained therein.)
This post complements John Omielan's accepted answer, and attempts to prove that $m \neq 0$ leads to the same desired conclusion, $k=1$. (Note: (August 11, 2022 - 5:10 PM Manila time) The desired conclu...
I have a question. My professor in the lecture said that Vinogradov's method by applying the Hardy-Littlewood circle method (minor and major arc) for the ternary Goldbach problem can be used to prove an "almost all" result for the Binary Goldbach problem. More precisely
Defining
$$ r(n) = \sum_{p...
Let $A,B \subset \Bbb{Z}$ be any subsets of the integers. We define $A - B = \{ a - b : a \in A, b \in B\}$ to be their elementwise difference. We define $\Delta A= A - A$. We define $A_{\geq n}$ to be the set of all $a \in A$ such that $a \geq n$.
Let $A = 2\Bbb{N} + 1$ be the odd numbers (wh...
Let $A,B \subset \Bbb{Z}$ be any subsets of the integers. We define $A - B = \{ a - b : a \in A, b \in B\}$ to be their elementwise difference. We define $\Delta A= A - A$. We define $A_{\geq n}$ to be the set of all $a \in A$ such that $a \geq n$.
Let $A = 2\Bbb{N} + 1$ be the odd numbers (wh...
