Draugiškasis skaičius

Iliustracija, kad skaičiai 220 ir 284 yra draugiškieji.

Draugiškieji skaičiai yra du natūriniai skaičiai, kurių kiekvienas lygus antrojo skaičiaus visų natūrinių daliklių, išskyrus patį skaičių, sumai. Pavyzdžiui: 220 ir 284 yra draugiškieji skaičiai, nes skaičiaus 220 daliklių suma yra

1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284,

o skaičiaus 284 daliklių suma yra

1 + 2 + 4 + 71 + 142 = 220.

Draugiškuosius skaičius galėtume apibrėžti ir kitaip: kiekvieno tokio skaičiaus visų daliklių suma yra lygi abiejų skaičių sumai.

Pirmosios penkios draugiškųjų skaičių poros yra: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368).

Istorija

Viena legenda pasakoja, kad Pitagoras, užklaustas, kas yra draugystė, atsakė: „220 ir 284“. Taip atsirado draugiškųjų skaičių pavadinimas. Leonardas Oileris vėliau rado 59 draugiškųjų skaičių poras.[1]

Šaltiniai

  1. K.Bulota, P.Survila. Algebra ir skaičių teorija. II dalis. – Vilnius: Mokslas, 1990. – 53 p. ISBN 5-420-00613-8

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