三个二次多项式的和a的n次方,n = (2,3,4,5,6,7,8 & 9)

S. Tomita, Oliver Couto
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引用次数: 0

摘要

考虑下面提到的等式:x4+y4+z4=w * tn----(A)。历史上,伦纳德·欧拉给出了方程(A)在w=1时的参数解(参考文献1)。9),度n =2。S. Realis也给出了当w = 1, n =3时方程(A)的参数解。更多的例子可以在数学文献(参考文献no.6)中找到。众所周知,求解大于4次的丢番图方程是困难的,本文的新颖之处在于我们做了一个系统的方法,并给出了不同w值的次n =(2,3,4,5,6,7,8,9)的参数解。论文分为A至H部分,分别代表学位(2至9)。x4 + y4 + z4 = w∗tn——()
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Sum of Three Biquadatics a Multiple of a n th Power, n = (2,3,4,5,6,7,8 & 9)
Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)
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