107.10 Trapezia whose side-lengths form an arithmetic progression

107.15 Fruit diophantine equation

“…-if is a prime, then by virtue of Wilson's theorem [1], n { (n − 1)! n } = n − 1 n -if is a composite different from 4, then divides and the braces evaluate to 0 [2].…”

“…The problem originated from the question "What is the smallest unsolved diophantine equation?" that was posed by user Zidane in MathOverflow [1]. In this question, the notion of size of a polynomial is the following one: for , define…”

107.14 Does a trapezium exist whose side lengths form a geometric progression?

“…The problem originated from the question "What is the smallest unsolved diophantine equation?" that was posed by user Zidane in MathOverflow [1]. In this question, the notion of size of a polynomial is the following one:…”

“…It is known that there is no trapezium whose lengths of consecutive sides form an arithmetic progression [1]. Is this true also for a geometric progression?…”