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The Green-Tao theorem states that for every $n$, there is an arithmetic sequence of length $n$ consisting of primes. For primes, $p$, let $P(p)$ be the maximum length of an arithmetic progression of ...

Let $A=(a_n : n \in \mathbb{N})$ be the sequence given by: $$ \ a_n = a_1 + (n - 1)d,\quad a_1,\ d,\ n \in \mathbb N,\quad d\gt a_1,\quad \gcd(a_1,\ d)=1. $$ For all terms of $A$ greater than $\ \...