By use of a Fourier-coefficient shift and subsequentz-transform, we employ the familiar process of replacing image trigonometric polynomials by polynomials in one or more variables. Among these polynomials we consider a «standard» type and define a «conjugation» on them. This conjugation has some of the same important properties as does the conjugation of complex numbers and this enables us to prove that the single concept which unifies the enumeration of phase ambiguities from amplitude data for images in any number of dimensions is «prime flipping». This reduces to «zero flipping» in the one-dimensional case. The presence of self-conjugate primes in the polynomial of an image does not lead to phase ambiguities, just as the presence of real zeros in the one-dimensional case does not produce such ambiguities. We show that all phase solution images which produce the same intensity must have the same integral band width.