An Elementary Proof of a Theorem About the Representation of Primes by Quadratic Forms
1954 ◽
Vol 6
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pp. 353-363
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Keyword(s):
The theorem that every properly primitive binary quadratic form is capable of representing infinitely many prime numbers was first proved completely by H. Weber (5). The purpose of this paper is to give an elementary proof of the case where the form is ax2 + 2bxy + cy2, with a > 0, (a, 2b, c) = 1, and D = b2 — ac not a square. The cases where the form is ax2 + bxy + cy2 with b odd, and the case where the form is ax2+ 2bxy + cy2 with D a square, can be settled very simply once the first case is taken care of, and this is done in a page and a half in the Weber paper.
1975 ◽
Vol 18
(1)
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pp. 123-125
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2019 ◽
Vol 16
(02)
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pp. 233-240
Keyword(s):
1929 ◽
Vol 125
(797)
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pp. 262-276
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1992 ◽
Vol 112
(1)
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pp. 7-19
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2010 ◽
Vol 54
(1)
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pp. 25-32
Keyword(s):
1945 ◽
Vol 41
(2)
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pp. 77-96
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2016 ◽
Vol 12
(03)
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pp. 679-690
Keyword(s):
1949 ◽
Vol 197
(1049)
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pp. 256-268
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Keyword(s):
1955 ◽
Vol 7
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pp. 337-346
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2007 ◽
Vol 03
(04)
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pp. 541-556
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