Chinese remainder theorem
The Chinese remainder theorem is a theorem of
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers.
There are certain things whose number is unknown. If we count them by threes, we have two left over; by fives, we have three left over; and by sevens, two are left over. How many things are there?
Sunzi's work contains neither a proof nor a full algorithm. What amounts to an algorithm for solving this problem was described by
The notion of congruences was first introduced and used by