Diophantine equations

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

The sum of the cubes of two numbers is 7163. What are these numbers?

Helen buys some cakes and some buns for her party. Can you work out how many of each she buys?

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

I am exactly n times my daughter's age. In m years I shall be ... How old am I?