Class number bounds and Catalan's equation
نویسنده
چکیده
We improve a criterion of Inkeri and show that if there is a solution to Catalan’s equation x − y = ±1, (1) with p and q prime numbers greater than 3 and both congruent to 3 (mod 4), then p and q form a double Wieferich pair. Further, we refine a result of Schwarz to obtain similar criteria when only one of the exponents is congruent to 3 (mod 4). Indeed, in light of the results proved here it is reasonable to suppose that if q ≡ 3 (mod 4), then p and q form a double Wieferich pair.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 67 شماره
صفحات -
تاریخ انتشار 1998