Number theory · Maths EE idea · Accessible
The Chinese remainder theorem and calendar cycles
A research question to start from
How does the Chinese remainder theorem explain when calendar cycles of different lengths coincide, and how can solutions be constructed efficiently?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A theorem with a constructive proof that you can apply to a context you choose, and an algorithm to evaluate.
Mathematics you would need
- Linear congruences
- The Euclidean algorithm and Bézout's identity
- The Chinese remainder theorem
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Prove the theorem and turn the proof into a construction.
- Apply it to cycles you choose (for example, weekly and lunar-style cycles, or planetary alignments with idealised periods).
- Handle moduli that are not coprime and say when there is no solution.
Scope and difficulty
Accessible. Accessible; make sure the context does not take over.
Pitfalls
- Context-heavy essay with thin mathematics.
- Assuming coprime moduli everywhere.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Chinese remainder theorem constructive proof; Bezout identity. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).