Mathematics of Computation

Author(s): Anastasios Simalarides.
Journal: Math. Comp. 71 (2002), 415-427.
MSC (2000): Primary 11C20; Secondary 11Y40, 11D79
Posted: October 18, 2000
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Let $c\geq 2$ be an even integer,

. The resultant

of the polynomials

and

is known as Wendt's determinant of order

. We prove that among the prime divisors

only those which divide

or $L_{c/2}$ can be larger than $\theta^{c/4}$ , where $\theta=2.2487338$ and

is the

th Lucas number, except when

and

. Using this estimate we derive criteria for the nonsolvability of Fermat's congruence.

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