Infinitely many minimal-integral integer polynomials of degree less than N are divisible by (x^3(1-x)^2)^{floor(N/6)} in Z[x].
Bazzanella,Integer polynomials with small integrals, Riv
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Another factor of integer polynomials with minimal integrals
Infinitely many minimal-integral integer polynomials of degree less than N are divisible by (x^3(1-x)^2)^{floor(N/6)} in Z[x].