Thue's Theorem

If ,  (i.e.,  and  are relatively prime), and  is the least integer , then there exist an  and  such that

where  and  (Nagell 1951, pp. 122-124; Shanks 1993, p. 161)

REFERENCES:

Nagell, T. "Thue's Remainder Theorem and Its Generalization by Scholtz." §36 in Introduction to Number Theory. New York: Wiley, pp. 122-124, 1951.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 161, 1993.