The assignment asks students to explore and investigate various number theory topics, including squares, modular arithmetic, quadratic residues, diagonals, Pythagorean triples, unit fractions, quadratic expressions, consecutive sums, stamp combinations, frog puzzles, square roots and continued fractions. Students are encouraged to develop their own patterns, make predictions, and generalize their findings. The assignment also includes some real-world applications, such as solving a problem involving odd socks.