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Wendt’s binomial circulant determinant, W„, is the determinant of an m by m circulant matrix of integers, with (i, j)th entry (i, ™.i) whenever 2 divides m but 3 does not. We explain how we found the prime factors of Wm for each even m < 200 by implementing a new method for computations in algebraic number fields that uses only modular arithmetic. As a consequence we prove that if p and q = mp + l are odd primes, 3 does not divide m, and m < 200, then the first case of Fermat’s Last Theorem is true for exponent p. © 1991 American Mathematical Society.

The prime factors of Wendt’s binomial circulant determinant