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Trinomials axn+bx+c with interesting Galois groups In 1969 Trinks discovered that the irreducible trinomial x7 - 7 x + 3, factored modulo small primes (other than the primes 3 and 7 dividing its discriminant 218), always yielded polynomials of degrees 7, 4+2+1, 3+3+1, or 2+2+1+1+1. This suggested that the trinomial had Galois group G168, the simple group of order 168 consisting of the invertible ...
www.math.harvard.edu/~elkies/trinomial.html
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