Two expressions that cannot both be cubes
For a natural number n, prove that n + 2 and n² + n + 1 cannot both be perfect cubes.
number theoryperfect powers
The notebook
All posts
Problems to solve, ideas to explore, and things to learn.
Finding an invisible spaceship
Can a fixed collection of detectors distinguish every possible 2 × 2 spaceship position on a 7 × 7 board?
combinatoricspuzzles
The average distance across a circle
Choose two points uniformly on a unit circle. What is their expected straight-line distance?
probabilitygeometryexpectation
A three-variable inequality
Prove a symmetric inequality for arbitrary real x, y, and z.
algebrainequalities
Trigonometry Without a Word
Two arctangent identities, seen through a geometric proof without words.
geometrytrigonometry