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?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Can you find a rule which relates triangular numbers to square numbers?
How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
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!
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?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?