Problem

TxO Math Bowl 2024 - Individuals B - Problem 6

Let $N$ be the number of subsets $S$ of $\{1, 2, 3, \dots, 2024\}$ such that $|S|$ has a remainder of $1$ when divided by $4$ . Given that $N$ can be expressed as $a^b$ , where $a$ and $b$ are positive integers such that $a$ is prime, find $a + b$ .

Note: $|S|$ denotes the number of elements in the set $S$ .

Show/Hide Problem Tags

Problem Tags: Number theory Set theory

Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)

Problem feedback

Difficulty —

Category: TxO Math Bowl Individual Round
Points: 4
Back to practice
Train more like this