Here’s a sample problem from discrete math when I took it in university:
For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd
number of parts, and each part is congruent to 1 modulo 3. Prove that:
|Cn| = [x^n] (x - x^4)/(1 - x^2 - 2x^3 + x^6)
Where [x^n] indicates the coefficient of the x^n term in the formal power series generated by the rational function (rational representation of the ordinary generating function).
I doubt many elementary school students would be able to solve problems like this.
And the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets).
There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.
You definitely don't need to know any of that background to be able to arrive at the answer. To fully understand everything maybe, but all it takes is:
The question doesn’t ask for an answer, it asks for a proof. You can’t just write a bunch of algebra and call it a day. You have to justify all of your arguments.
For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd number of parts, and each part is congruent to 1 modulo 3. Prove that:
Where [x^n] indicates the coefficient of the x^n term in the formal power series generated by the rational function (rational representation of the ordinary generating function).I doubt many elementary school students would be able to solve problems like this.