The diophantine problemY2−X3=Ain a polynomial ring
نویسندگان
چکیده
منابع مشابه
On Diophantine Sets over Polynomial Rings
We prove that the recursively enumerable relations over a polynomial ring R[t], where R is the ring of integers in a totally real number field, are exactly the Diophantine relations over R[t].
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The Greek mathematician Diophantus of Alexandria studied the following problem: Find four (positive rational) numbers such that the product of any two of them increased by 1 is a perfect square. He obtained the following solution: 1 16 , 33 16 , 17 4 , 105 16 (see [4]). Fermat obtained four positive integers satisfying the condition of the problem above: 1, 3, 8, 120. For example, 3 · 120+1 = 1...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1972
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1972.43.151