info prev up next book cdrom email home

Thue's Theorem

If $n>1$, $(a,n)=1$ (i.e., $a$ and $n$ are Relatively Prime), and $m$ is the least integer $>\sqrt{n}$, then there exist an $x$ and $y$ such that

\begin{displaymath}
ay\equiv \pm x\ \left({{\rm mod\ } {n}}\right)
\end{displaymath}

where $0<x<m$ and $0<y<m$.


References

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




© 1996-9 Eric W. Weisstein
1999-05-26