>> Let P(x) be a polynomial with integer coefficients such that, >> for each natural number _n_, P(n) is a perfect square. Does it >> follow that P(x) is the square of some polynomial with integer >> coefficients? > > Yes. > > My proof hinges on a key result which I call "The Sandwich > Theorem". It's an elementary result, definitely known, but > perhaps not well enough known. > > I independently discovered and proved this result when I was > in high school. > > I'll state the theorem and some corollaries, without proof for > now, but I'll supply proofs if requested.