Number 84

A page of the Numeropedia - the Special Encyclopedia of Numbers

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[Chemistry]  The atomic number of Polonium (Po).

[Chemistry]  Elements with atomic number 43 (Technetium, Tc), 61 (Promethium, Pm) and from 84 (Polonium, Po) up are radioactive.

[Library]  ISBN-84 is the International Standard Book Number for books published in Spain.

[Math.]  84 = 25+33+52.

[Math.]  A base system of multigrade equalities

1+5+10+18+23+27 = 84 = 2+3+13+15+25+26

12+52+102+182+232+272 = 1,708 = 22+32+132+152+252+262

13+53+103+183+233+273 = 38,808 = 23+33+133+153+253+263

14+54+104+184+234+274 = 926,884 = 24+34+134+154+254+264

15+55+105+185+235+275 = 22,777,944 = 25+35+135+155+255+265. (References [20])

Multigrade equalities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

[Math.]  1445 = 1335+1105+845+275. (Lander & Parkin, 1966). The first counter-example to disprove Euler’s conjecture that it always requires at least n terms (of nth power) to sum to an nth power, non-trivially. (Fermat’s Last Theorem is a special case for only 2 terms).

[Math.]

12×21 = 252 = 21×12

12×42 = 504 = 21×24          24×21 =    504 = 42×12

12×63 = 756 = 21×36          24×63 = 1,512 = 42×36

12×84 = 1,008 = 21×48       24×42 = 1,008 = 42×24

36×84 = 3,024 = 63×48       24×84 = 2,016 = 42×48.

[Movie]  Name of TV show/series or movie: “84 Charing Cross Road”.

[Phone]  International telephone dialing code for Vietnam.

[Science] The number 1045 is quattuordecillion, in American system. In British system, quattuordecillion is 1084.

[Sport] The minimal length of a basketball court is 84 feet = 25.60 meters.  The optimal length is 94 feet (= 28.65 meters) long.

[Tech.]  The “number system” code of an EAN-13 barcode for Spain’s products.

[World]  The ISO country code for Belize is 084. (ISO-3166)

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References [20]