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163


The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also satisfies the curious identities

163=sum_(i=0)^(4)(8; i)
(1)
=1/2[4^4+(8; 4)]
(2)
=1/2[4^4+sum_(i=0)^(4)(4; i)^2],
(3)

where (n; k) is a binomial coefficient.


See also

Ramanujan Constant

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References

Stoschek, E. "Modul 33: Algames with Numbers." n.d. http://marvin.sn.schule.de/~inftreff/modul33/task33.htm.

Cite this as:

Weisstein, Eric W. "163." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/163.html

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