The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for ra- tional sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this pa- per, we generalize Montgomery's method (12) using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also in- troduce GP of length d + k with 1 � kd 1 and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficientscan be precisely determined.