−3

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← −4 −3 −2 →
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Cardinal	negative three
Ordinal	-3rd (negative third)
Divisors	1, 3
Arabic	−٣
Bengali	−৩
Binary (byte)	11111101

In mathematics, negative three or minus three is an negative integer three units from the origin, denoted as −3 or ⁻3. It is the additive inverse of 3, positioned between −4 and −2. It is the second largest negative odd number.

Properties

• Negative three is a quadratic residue modulo 4.
• Negative three is the first, and smallest negated heegner number. only nine negative numbers have this property: −3, −4, −7, −8, −11, −19, −43, −67, −163.
• Negative three is the only negative integer whose Möbius function value appears as a fixed point of the map in the sequence 𝜇(𝑛) ∈ {−1,0,1}.
• The number negative three in the quadratic field $\mathbb{\mathbb{Q}}(\sqrt{-3})$ is its fundamental discriminant, and the ring of integers in this field is the lattice of Eisenstein integers.

${Z}[\omega ],\omega =\frac{-1+\sqrt{-3}}{2}$

Forming a perfect hexagonal (triangular) lattice in the plane.

• The quadratic field also has class number 1, meaning it behaves better as the integers for factoring.

Divisors of negative three

The divisors of the number negative three, including negative divisors, are identical to those of two: 1, 3, −1 −3. Since its only divisors are ±1 and ±3, negative three is considered an irreducible element, which is the equivalent of a prime number for negative integers.

See Also

• 3

References

This article "−3" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:−3. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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