# Questions tagged [arithmetic-progression]

An arithmetic progression is a (possibly infinite) sequence of numbers such that the difference between consecutive terms is always the same value.

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### On probability of equifactorable numbers in arithmetic progression

Let $T$ be a parameter. Fix $r$ with $|r|<T^{2x}$ and $A$ where $A>0$ is of size $T^{2x}$ where $x\in\{0,1\}$. Consider the set of integers of form $$r+kA$$ where $|k|$ is of size $T^{4x}$ ($k$ ...
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### Sum of squares squared in an arithmetic progression

Let $r(n)$ be the number of ways to write $n$ as a sum of two squares and $(a,q)=1$. What is known about $$\sum_{n \le x,n \equiv a (\text{mod} \, q)} r(n)^2 \quad?$$ I am looking for uniform ...
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### Primes in modular arithmetic progression

Fix a prime $p$. I want to get $k<p$ primes $p_1<\dots<p_k$ such that at every $i\in\{1,\dots,k\}$ we have $$p_i\equiv (2i+1+c)\bmod p$$ where $c$ is fixed and $2k+1+c<p$ holds. For a ...
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1 vote
Here discrepancy is from $(2.4)$ in https://www.ricam.oeaw.ac.at/files/people/siambook_nied.pdf given by 'The (extreme) discrepancy $D_N(P) = D_N(x_l,\dots,X_N)$ of the point set $P$ of $N$ points in $... 5 votes 1 answer 385 views ### Does every prime$p$appear in a$p$-term arithmetic progression of primes? [duplicate] This is a follow-up to an earlier question. The answer to that question was found on this page. The discussion on OEIS seems to suggest that, for any prime$p$, there should exist a$p$-length ... 29 votes 4 answers 3k views ### Is there an 11-term arithmetic progression of primes beginning with 11? i.e. does there exist an integer$C > 0$such that$11, 11 + C, ..., 11 + 10C$are all prime? 9 votes 1 answer 302 views ### A weak form of the Erdős-Turán conjecture This question is motivated by the answer of Gowers to the question Erdos Conjecture on arithmetic progressions. Question. (1)-Suppose$A \subset \mathbb{N}$is such that Lim$_nlog(n) \cdot |A \...
Consider the simple arithmetic progression ($s, z \in \mathbb{Z}$): $a_1 = s$ $a_{n+1} = a_n + z = s + n\cdot z$ Can somebody devise a procedure (another progression) $b_n$ so that there exists a \$...