2 April 2017

Four


Four color theorem by Kenneth Appel proves that a two-dimensional map, with some limitations, may be colored with four colors without any of the adjacent "countries" be painted with the same color.

A square with the side \(4\) has its perimeter equal to its area (without considering the units), ie, $16$.

Any whole number in the form \(n^4+4\) is not prime, except for the case \(n=1\), where \(n^4+4=\left(n^2-2n+2 \right) \left(n^2+2n+2 \right)\). In fact,  is the product of two composite numbers and it is also a composite number.

Any prime number in the form \(4k+1\) is the sum of two perfect squares. For example: \(13=4 \cdot  3+1=2^2+3^2\).

Multiplying \(21,978\) by \(4\), it reverses the order of its digits: \(21,978 \cdot 4= 87,912\).

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