Difference of two squares
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Difference of two squares
What is special about the difference between squares of numbers adjacent to multiples of three?
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2-digit square
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
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Odd differences
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.
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Plus minus
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
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What's possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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Why 24?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
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Particularly general
By proving these particular identities, prove the existence of general cases.
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Euler's squares
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
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DOTS division
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.