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Odd Differences

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

Note that 15 = 8² - 7² as well as 4² - 1².

Write the number 105 as the difference of two squares in as many different ways as you can?

The number 1155 can be written as the difference of two squares in eight different ways, can you find them?