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 = [画像:sum_(i=0)^(4)(8; i)]
(1)
= [画像:1/2[4^4+(8; 4)]]
![画像:1/2[4^4+(8; 4)]](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/163/Inline9.svg){kind=link}
(2)
![画像:1/2[4^4+sum_(i=0)^(4)(4; i)^2],](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/163/Inline12.svg){kind=link}
where (n; k) is a binomial coefficient.
See also
Ramanujan ConstantExplore with Wolfram|Alpha
WolframAlpha
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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 Resource. https://mathworld.wolfram.com/163.html