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Algebraic Integers

 

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196,883 dimensions

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163 and the Monster

 

An algebraic integer is a complex number that is the solution to an algebraic equation having leading coefficient 1, meaning that the coefficient of the highest power of x is 1. For example the equation x2 = 2 has leading coefficient 1, and its solutions, namely the square root of 2, and minus the square root of 2, are algebraic integers. On the other hand, the equation 2x = 1 has leading coefficient 2, and its solution, x = ½, is not an algebraic integer. An algebraic integer that is a real number must be an ordinary integer.

The entries in a character table are algebraic integers.