50 (number): Difference between revisions - Wikipedia

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{{Infobox number

| number = 50

50

| numeral = quinquagesimal

| divisor = 1, 2, 5, 10, 25, 50

| unicode = ↆ

|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ծ|lang2=[[Hebrew numerals|Hebrew]]|lang2 symbol=<span style="font-size:150%;">נ / ן</span>|lang3=[[Babylonian cuneiform numerals|Babylonian numeral]]|lang3 symbol=<span style="font-size:200%;">𒐐</span>|lang4=[[Egyptian numerals|Egyptian hieroglyph]]|lang4 symbol=<span style="font-size:200%;">𓎊</span>}}

'''50''' ('''fifty''') is the [[natural number]] following [[49 (number)|49]] and preceding [[51 (number)|51]].

==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 (seethe imageformer is the sum of squares of divisors of [[7]]).<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 (that feature in the smallest [[Pythagorean triple]]), and the sum of four squares, 50 = 6² + 3² + 2² + 1². It is(as the sum of the [[Square number|squares]] of the [[divisor]]sdivisors 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>