What is the smallest perfect square that ends with the four digits 9009?

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Find the shape and symmetries of the two pieces of this cut cube.

The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n + x^n = (x+1)^n so what about other solutions for x an integer and n= 2, 3, 4 or 5?

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?