let' s define 'height' of a polynomial the max of the absolute value of its coefficients.
Do exist P(x) and Q(x) TWO polynomials at integer coefficient with heights equal or greater than 2011, whose product is a polynomial with height =1?
I have tried with cyclotomic polynomials, that we know can have any coefficient among the integers, and whose product of convenient cyclotomic gives x^n-1 (whoe height is 1), but I cannot demonstrate that I can find exactlky TWO polynomials whith height >=2011 whose product is a polyn. with height=1.
has anyone a clue onhow to solve with cyclotomic or with any other method?