You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.
Displaying 1131 - 1140 of 1209
The number \(2\) is a quadratic residue mod \(p\) if \(p = 8k + 1\) or \(p = 8k + 7\), but not if \(p = 8k + 3\) or \(p = 8k + 5\). This is proved by a simple counting argument, assuming the...
Given a positive integer \(m\), the authors exhibit a group with the probability \(1/m\) that two randomly selected elements commute.
The number of black squares in a crossword puzzle, and the number of marks needed to bound the black squares allows one to determine the number of words the puzzle contains.
In this note an elementary proof of Stirling's asymptotic formula for \(n!\) is given.
The authors explain certain inequalities visually.
A Fibonacci identity is depicted visually.
Using just very basic knowledge of finite fields and the inclusion-exclusion formula, the authors show how one can see the shape of Gauss` formula for the number of irreducible polynomials of...