WebThe general primitive solution in integers of the equation x 2 + 3 y 2 = N 3 for odd N is given by x = u ( u 2 − 9 v 2) and y = 3 v ( u 2 − v 2) where u and v are co-prime integers. If an … WebNov 15, 2009 · Let n be a square-free polynomial over F_q, where q is an odd prime power. In this paper, we determine which irreducible polynomials p in F_q[x] can be represented in …

Primes of the form $x^2+ny^2$ and congruences. - MathOverflow

WebNov 1, 2016 · 5. Check out the book by Cox: Primes of the form x 2 + n y 2. In this book, Theorem 9.2 gives a reasonable description of primes of the form p = x 2 + n y 2. I believe the same result (and proof) works verbatim when n is replaced by − n in this theorem. The only difference is that if a prime can be written as x 2 − n y 2, then it can be ... Web1 day ago · L’amour est dans le pré : Lucile et Jérôme dévoilent le sexe de leur bébé ! china veasey

PRIMES IN THE FORM ⌊αp + β⌋ Semantic Scholar

WebExpress your answer in the form m = 0 ∑ ∞ b m x m − 2 + m = 0 ∑ ∞ c m x m = 0, where b m and c m are to be written in terms of m and a m . 3. Shift the index on one of the series you found in 2 so that the exponents of x are equal to m in both series. WebLet β be a real number. Then for almost all irrational α > 0 (in the sense of Lebesgue measure) lim sup x→∞ π∗ α,β(x)(log x) /x ≥ 1, where π∗ α,β(x) = {p ≤ x : both p and ⌊αp + β⌋ are primes}. Recently Jia [4] solved a conjecture of Long and showed that for any irrational number α > 0, there exist infinitely many primes not in the form 2n+ 2⌊αn⌋ + 1, where ⌊x ... Web$\begingroup$ It will not be very quick. You can easily identify the congruence classes which are not ruled out. But to show each of the non-forbidden primes is actually representable … china vast land