Gifted Mathematics

Find, with proof, all solutions of the equation 2 n = a! + b! + c! in positive integers a, b, c and n. (Here, ! means "factorial...

The image shows two regular octagons, each has 4 red and 4 blue beads, one placed on each vertex. We say that there is a 'match'...

Let N = a! + b! Find all solutions (a,b) such that N is divisible by 11 and both a and b are positive integers less than 11, with a ≤ b. ...

Six beads are arranged at the corners of a regular hexagon; 3 are orange and 3 green. All arrangements that are rotational symmetries of ...

Prove that in each set of ten consecutive integers there is one which is coprime with each of the other integers. For example, taking 114...