Math Olympiad — Number Theory Fundamentals + 4 more topics

Math Olympiad problems often look intimidating at first glance because they don't have a clear, obvious path to the solution. That's where strategies come in. They give you a structured way to start, even when you feel stuck.

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Number theory focuses on integers: ..., -3, -2, -1, 0, 1, 2, 3, ...

For example:
* 3 | 12 because 12 / 3 = 4 (an integer).
* 5 <binary data, 1 bytes> 12 because 12 / 5 = 2.4 (not an integer).

Key properties of divisibility:
* If a | b and b | c, then a | c (transitivity).
* If a | b and a | c, then a | (bx + cy) for any integers x, y. This is really powerful!

You'll often hear about permutations and combinations. The main difference is whether order matters.

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Math Olympiad algebra often involves more than just basic equation solving. It's about seeing the underlying structure and using powerful techniques to simplify or transform expressions.

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You'll often find yourself switching between Euclidean and coordinate geometry. Euclidean methods are great for proofs involving angles, congruency, and similarity, while coordinate methods are powerful for finding distances, slopes, areas, and dealing with equations of lines and circles.