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Upper Bounds for the Prime Divisors of Wendt's Determinant

Anastasios Simalarides
Mathematics of Computation
Vol. 71, No. 237 (Jan., 2002), pp. 415-427
Stable URL: http://www.jstor.org/stable/2698883
Page Count: 13
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Upper Bounds for the Prime Divisors of Wendt's Determinant
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Abstract

Let c ≥ 2 be an even integer, (3, c) = 1. The resultant Wc of the polynomials tc - 1 and (1 + t)c - 1 is known as Wendt's determinant of order c. We prove that among the prime divisors q of Wc only those which divide 2c- 1 or Lc/2 can be larger than θc/4, where θ = 2.2487338 and Ln is the nth Lucas number, except when c = 20 and q = 61. Using this estimate we derive criteria for the nonsolvability of Fermat's congruence.

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