
 Some math, algebraic integers (Site not responding. Last check: 20071106) 
  By contrast, and algebraic integer is a complex number which is the root of a monic polynomial with INTEGER coefficients. 
  At any rate, it's evident that there are algebraic integer factors in common with q_1 and 2, and that those factors cannot be units in the ring of algebraic integers. 
  With algebraic integers, it's a little more complicated as if x and y are irrational, and, get this, are roots of a nonmonic quadratic with integer coefficients irreducible over rationals, then *apparently* both x and y must have factors in common with 2. 
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