Cancellation Law

If $bc\equiv bd\ \left({{\rm mod\ } {a}}\right)$ and $(b,a)=1$ (i.e., $a$ and $b$ are Relatively Prime), then $c\equiv d\ \left({{\rm mod\ } {a}}\right)$.

See also Congruence

References

Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 36, 1996.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 56, 1993.