We characterize irreducible trinomials x 6 + Ax + B with coefficients in a number field K which have Galois group C 6 , S 3 or C 3 × S 3 . This characterization relates these trinomials to the K-rational points on a genus 2 curve. We determine these trinomials explicitly in the case K = ℚ.
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Brown et al. (2012) studied this question.