Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
Can you find a rule which relates triangular numbers to square numbers?
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Which numbers can we write as a sum of square numbers?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?