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.
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.