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Representing integers as the sum of two squares

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Almost 400 years ago, Pierre de Fermat stated that every odd prime of the form `4k+1` can be expressed as the sum of two squares:

`p = x^2 + y^2`

with integers `x` and `y`, if and only if

`p ≡ 1 mod 4`

Later on, around the year 1747, Leonhard Euler was able to prove Fermat's statement correct.

Representing integers as the difference of two squares

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Most integers can be represented as a difference of two squares, where each square is a non-negative integer.