Abstract
In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) <TEX>${\in}$</TEX> <TEX>$\mathbb{Q}$</TEX>[x], <TEX>$f{\circ}g$</TEX> is reducible over <TEX>$\mathbb{Q}$</TEX> for an irreducible polynomial g(x) <TEX>${\in}$</TEX> <TEX>$\mathbb{Q}$</TEX>[x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that <TEX>$f{\cric}f$</TEX> is reducible. We construct a system of infitely many such polynomials.
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