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- W2100069168 abstract "Nagell [5] confirmed a conjecture of Ramanujan [6] that the solutions of equation x + 7 = 2 in integers x > 0, n > 0 are given by (x, n) = (1, 3), (3, 4), (5, 5), (11, 7), (181, 15). This result implies that the solutions of equation (1) with x = 2 and n = 3 are given by (2). Perhaps equation (1) has no solution other than the ones given by (2). Shorey [10] proved that 31 and 8191 are the only primes N such that N has all the digits equal to 1 with respect to two distinct bases and ω(N−1) ≤ 5. Here ω(N − 1) denotes the number of distinct prime divisors of N − 1. We re-write equation (1) as" @default.
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- W2100069168 date "1998-01-01" @default.
- W2100069168 modified "2023-09-27" @default.
- W2100069168 title "On an equation of Goormaghtigh" @default.
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- W2100069168 doi "https://doi.org/10.4064/aa-83-4-381-389" @default.
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