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Shades of Fermat's Last Theorem

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?

Rudolff's Problem

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?

BT.. Eat Your Heart Out

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?

Upsetting Pitagoras

Age 14 to 18 Challenge Level:

Find the smallest integer solution to the following equation:

$$\frac {1}{x^2}+\frac {1}{y^2}=\frac {1}{z^2}$$