Square numbers

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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?

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?