NP-Harp

Recall, in our discussion of the Church-Turing thesis, that we introduced the language D = {p | p is a polynomial in several variables having an integral root}.  We stated, but didn’t prove, that D is undecidable.  In this problem you are to prove a different property of D, namely, that D is NP-hard.  A problem is NP-hard if all problems in NP are polynomial time reducible to it, even though it may not be in NP itself.  So, you must show that all problems in NP are polynomial time reducible to D.