50 (number): Difference between revisions - Wikipedia

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==In mathematics==

[[File:square-sum-50.png|thumb|50 as the sum of two non-zero squares]]

Fifty is the smallest number that is the sum of two non-zero [[square numbers]] in two distinct ways: 50 = 1² + 7² = 5² + 5² (see image).<ref>de Koninck, J.M. (2009). ''Those fascinating numbers''. AMS Bookstore. p. 18. {{ISBN|0-8218-4807-0}}.</ref> It is also the sum of three squares, 50 = 3² + 4² + 5², and the sum of four squares, 50 = 6² + 3² + 2² + 1². It is a [[Harshad number]].<ref>{{Cite web|url=https://oeis.org/A005349|title=Sloane's A005349 : Niven (or Harshad) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}</ref> It is the sum of the [[Square number|squares]] of the [[divisor]]s of both [[6]] and [[7]].<ref>{{Cite OEIS |A001157 |a(n) as sigma_2(n): sum of squares of divisors of n. |access-date=2024-07-21 }}</ref>

50 is a [[Stirling number of the first kind]]: <math>\left[{5\atop 2}\right] = 50</math> and also a [[Narayana number]]: <math>\operatorname{N}(6, 3) = \operatorname{N}(6, 4) = 50</math>