Pisot and Vijayaraghavan
studied numbers whose m-th power is nearly an integer ín the sense that the
discrepancy vanishes as m becomes infinite. One plus square root two is an example.
Algebraic numbers of this type are characterized as algebraic integers whose
conjugate roots each have absolute value less than one. This note develops a test for
this property. An algorithm is given which determines whether or not one root of a
polynomiaI has absolute value greater than one and all the other roots have absolute
value less than one. If n is the degree of the polynomial, this algorithm involves only
n rational steps.
