Given a polynomial with integer roots, is it possible to add an integer to the polynomial so the roots of the new polynomial are also integers.
Apparently it is possible for some polynomials.
For example $$ x^2-6x+5$$ and $$x^2-6x+8$$ satisfy our conditions.
Third order polynomials such as $$x^3-12x^2+41x-30$$ and $$x^3-12x+41x-42$$ satisfy the conditions as well.
My question is what is the highest possible degree of polynomials satisfying the said conditions.
from Hot Weekly Questions - Mathematics Stack Exchange
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