TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS
TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS
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DOI：
10.1142/s1793042111004496
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发表时间：
2011-11
影响因子：
0.7
通讯作者：
T. Miyazaki
中科院分区：
文献类型：
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作者：
T. Miyazaki
设a、b、c为互素正整数，使得ap + bq = cr，且固定整数p、q、r ≥ 2。Terai推测方程ax + by = cz除特殊情况外，除了(x, y, z) = (p, q, r)外，没有正积分解。该猜想的大多数已知结果涉及 p = q = 2 且 r = 2 或奇数 r ≥3 的情况。在本文中，我们考虑p = q = 2且r > 2为偶数的情况，并部分验证Terai的猜想。
Let a, b, c be relatively prime positive integers such that ap + bq = cr with fixed integers p, q, r ≥ 2. Terai conjectured that the equation ax + by = cz has no positive integral solutions other than (x, y, z) = (p, q, r) except for specific cases. Most known results on this conjecture concern the case where p = q = 2 and either r = 2 or odd r ≥3. In this paper, we consider the case where p = q = 2 and r > 2 is even, and partially verify Terai's conjecture.