Number Theory Crossword
Solve 18 number theory clues — primes, factors, modular arithmetic, sequences, and more. Complete each word to unlock an encyclopedic definition.
How to Play
- Click a white cell to select it — click again to toggle Across/Down.
- Type a letter; the cursor advances automatically.
- Use arrow keys to move; Tab jumps to the next word.
- Click a clue in the list to jump to that word.
- Press Check Answers for correct (green) and wrong (red) cells.
- Reveal Word fills the current word (−50 pts penalty).
- Complete a word to unlock its encyclopedic definition!
Building your crossword…
Number Theory: Vocabulary of the Integers
Number theory is the branch of mathematics devoted to studying the properties and relationships of integers. Its concepts — primes, divisibility, modular arithmetic — seem abstract but underlie everything from everyday fraction arithmetic to the cryptographic systems protecting all digital communication.
Prime Numbers
Divisible only by 1 and themselves — the building blocks of all integers. The Fundamental Theorem of Arithmetic guarantees every integer has a unique prime factorization. RSA encryption relies on the difficulty of factoring large products of two primes.
Divisibility
One integer divides another evenly when the remainder is zero. Divisibility rules provide shortcuts for mental math; modular arithmetic generalizes divisibility to the mathematics of remainders.
Modular Arithmetic
Arithmetic that wraps around at a modulus — like a clock at 12 hours. Written a ≡ b (mod m). Modular arithmetic is the mathematical foundation of all modern digital cryptography and security.
Sequences
Ordered lists of numbers following a defined rule — arithmetic (constant difference), geometric (constant ratio), or recursive (each term defined by previous terms, like Fibonacci). Sequences model discrete change.
Logarithm
The inverse of exponentiation. Logarithms compress enormous ranges into manageable scales. The Richter, decibel, pH, and stellar magnitude scales are all logarithmic — a single unit change represents a 10× or more change in the underlying quantity.
Binary
The base-2 number system using only 0 and 1 — the universal language of digital computing. Every piece of data in every computer is ultimately a binary sequence. Powers of 2 define storage and memory sizes.