*The author presents three solutions to a problem concerning the terms of a certain linear recurrence modulo prime numbers.*

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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...*