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- Idoneal_number abstract "In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime, prime power, twice one of these, or a power of 2. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.A positive integer n is idoneal if and only if it cannot be written as ab + bc + ac for distinct positive integer a, b, and c.It is sufficient to consider the set { n + k2 | k2 ≤ 3 · n ∧ gcd (n, k) = 1 }; if all these numbers are of the form p, p2 , 2 · p or 2s for some integer s, where p is a prime, then n is idoneal.The 65 idoneal numbers found by Carl Friedrich Gauss and Leonhard Euler and conjectured to be the only such numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130, 133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, and 1848 (sequence A000926 in OEIS). In 1973, Peter J. Weinberger proved that at most one other idoneal number exists, and that the list above is complete if the generalized Riemann hypothesis holds.".
- Idoneal_number wikiPageExternalLink 0312440.
- Idoneal_number wikiPageExternalLink 0507352.
- Idoneal_number wikiPageExternalLink kmath058.htm.
- Idoneal_number wikiPageID "14556621".
- Idoneal_number wikiPageLength "3802".
- Idoneal_number wikiPageOutDegree "14".
- Idoneal_number wikiPageRevisionID "675021919".
- Idoneal_number wikiPageWikiLink André_Weil.
- Idoneal_number wikiPageWikiLink Carl_Friedrich_Gauss.
- Idoneal_number wikiPageWikiLink Category:Integer_sequences.
- Idoneal_number wikiPageWikiLink Category:Unsolved_problems_in_mathematics.
- Idoneal_number wikiPageWikiLink Coprime_integers.
- Idoneal_number wikiPageWikiLink Eulers_factorization_method.
- Idoneal_number wikiPageWikiLink Generalized_Riemann_hypothesis.
- Idoneal_number wikiPageWikiLink Greatest_common_divisor.
- Idoneal_number wikiPageWikiLink Leonhard_Euler.
- Idoneal_number wikiPageWikiLink List_of_unsolved_problems_in_mathematics.
- Idoneal_number wikiPageWikiLink Paulo_Ribenboim.
- Idoneal_number wikiPageWikiLink Peter_J._Weinberger.
- Idoneal_number wikiPageWikiLink Prime_number.
- Idoneal_number wikiPageWikiLinkText "Idoneal number".
- Idoneal_number wikiPageWikiLinkText "idoneal number".
- Idoneal_number title "Idoneal Number".
- Idoneal_number urlname "IdonealNumber".
- Idoneal_number wikiPageUsesTemplate Template:!.
- Idoneal_number wikiPageUsesTemplate Template:=.
- Idoneal_number wikiPageUsesTemplate Template:Classes_of_natural_numbers.
- Idoneal_number wikiPageUsesTemplate Template:Math.
- Idoneal_number wikiPageUsesTemplate Template:Math-stub.
- Idoneal_number wikiPageUsesTemplate Template:MathWorld.
- Idoneal_number wikiPageUsesTemplate Template:OEIS.
- Idoneal_number subject Category:Integer_sequences.
- Idoneal_number subject Category:Unsolved_problems_in_mathematics.
- Idoneal_number hypernym D.
- Idoneal_number type VideoGame.
- Idoneal_number type Combinatoric.
- Idoneal_number type Integer.
- Idoneal_number comment "In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime, prime power, twice one of these, or a power of 2. In particular, a number that has two distinct representations as a sum of two squares is composite.".
- Idoneal_number label "Idoneal number".
- Idoneal_number sameAs Q3879415.
- Idoneal_number sameAs Nombres_idonis_dEuler.
- Idoneal_number sameAs Número_idóneo.
- Idoneal_number sameAs Numero_idoneo.
- Idoneal_number sameAs m.03d7tqw.
- Idoneal_number sameAs Q3879415.
- Idoneal_number wasDerivedFrom Idoneal_number?oldid=675021919.
- Idoneal_number isPrimaryTopicOf Idoneal_number.