Diophantine equation X 4+Y 4 = 2(U 4 + V 4)
نویسندگان
چکیده
منابع مشابه
ON THE DIOPHANTINE EQUATION x 4 − q 4 = py 5
In this paper we study the Diophantine equation x4− q4 = py5, with the following conditions: p and q are different prime natural numbers, y is not divisible with p, p ≡ 3 (mod20), q ≡ 4 (mod5), p is a generator of the group (
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In this paper, we prove a theorem about the integer solutions to the Diophantine equation x − q = py, extending previous work of K.Győry, and F.Luca and A.Togbe, and of the author. MSC (2000): 11D41
متن کاملON THE DIOPHANTINE EQUATION x 4 − q 4 = py 3
In this paper we study the Diophantine equation x4−q4 = py, with the following conditions: p and q are prime distincts natural numbers, x is not divisible with p, p ≡ 11 (mod12), q ≡ 1 (mod3), p is a generator of the group ( Zq , · ) , 2 is a cubic residue mod q.
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The quadruple (1 484 801, 1 203 120, 1 169 407, 1 157 520) already known is essentially the only non-trivial solution of the Diophantine equation x4 + 2y4 = z4 + 4w4 for |x|, |y|, |z|, and |w| up to one hundred million. We describe the algorithm we used in order to establish this result, thereby explaining a number of improvements to our original approach [EJ].
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A survey is presented of the more important solution methods of the equation of the title. When space permits, a brief description of the methods and numerical examples are also given. The paper concludes with an incomplete list of 218 primitive nontrivial solutions in rational integers not exceeding 106.
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ژورنال
عنوان ژورنال: Mathematica Slovaca
سال: 2016
ISSN: 1337-2211,0139-9918
DOI: 10.1515/ms-2015-0157