具有四项的指数丢番图方程(Ⅱ) |
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引用本文: | 莫德泽.具有四项的指数丢番图方程(Ⅱ)[J].数学学报,1994,37(4):482-490. |
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作者姓名: | 莫德泽 |
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作者单位: | 湛江师范学院数学系!湛江524048 |
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摘 要: | 本文中,我们给出了丢番图方程的解x,y,z,w的上界,其中p,q是给定的互素的正整数,a,b,c,d是给定的适合abed≠0的整数,此外,我们将指出在具体情形下如何把上界降低到方程允许的实际的解.最后,我们将用这个方法来解方程19.5x·17y=12.5z+41.17w+14, 5. 3x· 13y + 20= 7. 3z + 14. 13w和 13· 2x+ 5· 3y= 25. 2z+ 11. 3w.
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关 键 词: | 丢番图方程 丢番图方程解的上界 丢番图方程的解 p-adic数的展开式 |
收稿时间: | 1991-12-23 |
修稿时间: | 1993-1-5 |
Exponential Diophantine Equations with Four Terms (II) |
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Institution: | Mo Deze (Zhanjiang Teacher's College of Guangdong, Zhanjiang 524048, China) |
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Abstract: | In this paper the upper bounds for the solutions x, y, z, w to the diophantine equations apxqy + bpz + cqw + d = 0 and apx + bqy + cpz + dqw = 0 are computed, where p, q are given to be fixed relatively prime positive integers and a, b, c, d integers with abed ≠ 0. Also, we show the upper bounds in a particular case can be reduced to allow the practical solution of the equation. Finally, we use the method to solve the equations 19× 5x17y = 12 × 5z +41 ×17w + 14, 5 × 3x13y + 20 = 7 ×3z + 14× 13w and 13 × 2x + 5× 3y = 25× 2z + 11× 3w. |
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