Beyond Schur's Conjecture

Vinogradov's Conjecture and Beyond

“…rr nr rn nn rrr rrn nrr nrn rnr rnn nnr nnn From the above note, we can see that, the number of 2-arithmetic progressions of quadratic residues is exactly p−3 4 . In 2016 [15], we have proved the following.…”

“…Theorem 2.3. [15] For p ≡ 3 (mod 4) the number of 3−arithmetic progressions of quadratic residues with common difference d is exactly ⌊ p−3 8 ⌋ for every d ∈ Z p \{0}.…”