Hilbert number ( $4 k + 1$ )

A Hilbert number is a positive integer congruent to

1

4

. The Hilbert numbers form a multiplicative set: a product of two of them is again congruent to

1

4

.

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- Squarefree Hilbert number Hilbert number

Squarefree Hilbert number

In the multiplicative set of Hilbert numbers, a squarefree Hilbert number is one divisible by no square

h^{2}

of a Hilbert number

h > 1

. This is weaker than being a squarefree integer:

9

is a squarefree Hilbert number because its square divisor

9 = 3^{2}

has

3

outside the Hilbert numbers.

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The Hilbert number is generally associated with the concept of the Hilbert space and refers to a specific enumeration of points in such spaces. However, in a more concrete mathematical context, "Hilbert numbers" are often used to refer to certain types of sequences or series associated with the work of the mathematician David Hilbert, particularly in relation to cardinalities, sets, and various hierarchies within mathematical analysis or topology.

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