Difference of two squares

There are 11 NRICH Mathematical resources connected to Difference of two squares
Hollow Squares
problem
Favourite

Hollow squares

Age
14 to 16
Challenge level
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Which armies can be arranged in hollow square fighting formations?
Difference of Two Squares
problem
Favourite

Difference of two squares

Age
14 to 16
Challenge level
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What is special about the difference between squares of numbers adjacent to multiples of three?
2-Digit Square
problem
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2-digit square

Age
14 to 16
Challenge level
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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?
Odd Differences
problem
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Odd differences

Age
14 to 16
Challenge level
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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.
Plus Minus
problem
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Plus minus

Age
14 to 16
Challenge level
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Can you explain the surprising results Jo found when she calculated the difference between square numbers?
What's Possible?
problem
Favourite

What's possible?

Age
14 to 16
Challenge level
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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Why 24?
problem
Favourite

Why 24?

Age
14 to 16
Challenge level
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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.
Particularly general
problem

Particularly general

Age
16 to 18
Challenge level
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By proving these particular identities, prove the existence of general cases.
Euler's Squares
problem

Euler's squares

Age
14 to 16
Challenge level
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Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
DOTS Division
problem

DOTS division

Age
14 to 16
Challenge level
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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}.