Quiz (Test MathJax)
Published:
We consider polynomials whose degree and coefficients satisfy a natural number constraint involving their sum. By fixing the degree, the problem reduces to counting compositions of an integer into positive parts, which can be solved using the stars-and-bars method. The number of solutions for each fixed degree corresponds to a binomial coefficient, and summing over all possible degrees yields a power of two. Consequently, the total number of admissible polynomials is given by an exponential expression.