7 To The Fifth Power

The result of multiplying five instances of a number together

In arithmetic and algebra, the fifth power or sursolid ^[1] of a number n is the consequence of multiplying five instances of north together:

north ⁵ = north × n × n × n × northward .

Fifth powers are also formed past multiplying a number by its quaternary power, or the square of a number past its cube.

The sequence of fifth powers of integers is:

0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, 161051, 248832, 371293, 537824, 759375, 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625, ... (sequence A000584 in the OEIS)

Backdrop [edit]

For whatsoever integer n, the last decimal digit of n ⁵ is the aforementioned as the last (decimal) digit of due north. I.E:

${\displaystyle n\equiv north^{v}{\pmod {10}}}$

Past the Abel–Ruffini theorem, there is no general algebraic formula (formula expressed in terms of radical expressions) for the solution of polynomial equations containing a fifth power of the unknown as their highest power. This is the lowest power for which this is truthful. See quintic equation, sextic equation, and septic equation.

Along with the 4th power, the 5th ability is one of two powers k that tin be expressed every bit the sum of one thousand − 1 other k-th powers, providing counterexamples to Euler's sum of powers conjecture. Specifically,

27⁵ + 84⁵ + 110⁵ + 133⁵ = 144⁵ (Lander & Parkin, 1966)^[2]

Come across also [edit]

• Seventh ability
• Sixth ability
• Fourth ability
• Cube (algebra)
• Square (algebra)
• Perfect power

Footnotes [edit]

1. ^ "Webster's 1913".
2. ^ Lander, Fifty. J.; Parkin, T. R. (1966). "Counterexample to Euler'south conjecture on sums of like powers". Bull. Amer. Math. Soc. 72 (6): 1079. doi:10.1090/S0002-9904-1966-11654-3.

References [edit]

• Råde, Lennart; Westergren, Bertil (2000). Springers mathematische Formeln: Taschenbuch für Ingenieure, Naturwissenschaftler, Informatiker, Wirtschaftswissenschaftler (in German) (three ed.). Springer-Verlag. p. 44. ISBN3-540-67505-ane.
• Vega, Georg (1783). Logarithmische, trigonometrische, und andere zum Gebrauche der Mathematik eingerichtete Tafeln und Formeln (in German). Vienna: Gedruckt bey Johann Thomas Edlen von Trattnern, kaiferl. königl. Hofbuchdruckern und Buchhändlern. p. 358. 1 32 243 1024.
• Jahn, Gustav Adolph (1839). Tafeln der Quadrat- und Kubikwurzeln aller Zahlen von one bis 25500, der Quadratzahlen aller Zahlen von 1 bis 27000 und der Kubikzahlen aller Zahlen von one bis 24000 (in German language). Leipzig: Verlag von Johann Ambrosius Barth. p. 241.
• Deza, Elena; Deza, Michel (2012). Figurate Numbers. Singapore: World Scientific Publishing. p. 173. ISBN978-981-4355-48-iii.
• Rosen, Kenneth H.; Michaels, John G. (2000). Handbook of Discrete and Combinatorial Mathematics. Boca Raton, Florida: CRC Press. p. 159. ISBN0-8493-0149-ane.
• Prändel, Johann Georg (1815). Arithmetik in weiterer Bedeutung, oder Zahlen- und Buchstabenrechnung in einem Lehrkurse - mit Tabellen über verschiedene Münzsorten, Gewichte und Ellenmaaße und einer kleinen Erdglobuslehre (in German). Munich. p. 264.

7 To The Fifth Power,

Source: https://en.wikipedia.org/wiki/Fifth_power_(algebra)

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