Sun Tzu Suan Ching/Examples/Example 2
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Example of Problem from Sun Tzu Suan Ching
- There are certain things whose number is unknown.
- Repeatedly divided by $3$, the remainder is $2$;
- by $5$ the remainder is $3$,
- and by $7$ the remainder is $2$.
- What will be the number?
Solution
The number of objects could be any one of the numbers:
- $23 + 105 n$
where $n \in \N$ is an arbitrary natural number.
Proof
From Chinese Remainder Theorem: $x \equiv 2 \pmod 3, 3 \pmod 5, 2 \pmod 7$ we have that:
- $x \equiv 23 \pmod {105}$
The result follows.
$\blacksquare$
Sources
- c. 280 -- 473: Sun Tzu: Sun Tzu Suan Ching
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Sun Tsu Suan Ching: $70$