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A306929
Numbers k (>0) such that x^2+y^2 and x^2+k*y^2 can be simultaneously squares.
2
1, 7, 10, 11, 17, 20, 22, 23, 24, 27, 30, 31, 34, 41, 42, 45, 47, 49, 50, 52, 53, 57, 58, 59, 60, 61, 68, 71, 72, 74, 76, 77, 79, 82, 83, 85, 86, 90, 92, 93, 94, 97, 99, 100, 101, 102, 104, 105, 107, 110, 111, 112, 113, 114, 115, 119, 120, 121, 122, 124, 126, 127, 130, 133, 134, 137
OFFSET
1,2
COMMENTS
Note that Dickson refers to C. H. Brooks and S. Watson, 1857 and lists "the following 41 positive integers A<=100." but 47, 53 and 83 are missing. - Michael Somos, Feb 09 2020
REFERENCES
The Lady's and Gentleman's Diary, London, 1857, pp. 61-63. See question 1911.
LINKS
L. E. Dickson, History of the Theory of Numbers, vol. 2. Carnegie Institute Public. 256, Washington, DC, 1920, see p. 475.
K. S. Brown, Concordant Forms
EXAMPLE
From Seiichi Manyama, Jul 15 2019: (Start)
14663^2 + 111384^2 = 112345^2 and 14663^2 + 47*111384^2 = 763751^2. So 47 is a term.
2873161^2 + 2401080^2 = 3744361^2 and 2873161^2 + 83*2401080^2 = 22062761^2. So 83 is a term. (End)
From the K. S. Brown link, 1141^2 + 13260^2 = 13309^2, 1141^2 + 53*13260^2 = 96541^2, so 53 is a term. - Michael Somos, Feb 10 2020
CROSSREFS
Sequence in context: A088769 A057986 A274204 * A105140 A107018 A247868
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 16 2019
EXTENSIONS
More terms from Seiichi Manyama, Jul 15 2019
STATUS
approved