Posted On: 12/04/2012 9:21:05 PM
Post# of 72447
had to bring this here
biomanbaba
Tuesday, December 04, 2012 9:14:09 PM
Re: TheProgressive post# 12674
Post # of 12677
yeah I am a DIME AWAY from my FIRST DOUBLE HERE..but that is a beginning.....after that I look forward to the SQUARE and the CUBE
and then
This article is about mathematics. For mass media, see Political media.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So:
n4 = n × n × n × n
Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.
The sequence of fourth powers of integers (also known as biquadratic numbers or tesseractic numbers) is:
1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, ... (sequence A000583 in OEIS)
The last two digits of a fourth power of an integer can be easily shown (for instance, by computing the squares of possible last two digits of square numbers) to be restricted to only twelve possibilities:
00, 01, 16, 21, 25, 36, 41, 56, 61, 76, 81, 96
Every positive integer can be expressed as the sum of at most 19 fourth powers; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers (see Waring's problem).
Euler conjectured a fourth power cannot be written as the sum of 3 smaller fourth powers, but 200 years later this was disproven with:
958004 + 2175194 + 4145604 = 4224814.
biomanbaba
Tuesday, December 04, 2012 9:14:09 PM
Re: TheProgressive post# 12674
Post # of 12677
yeah I am a DIME AWAY from my FIRST DOUBLE HERE..but that is a beginning.....after that I look forward to the SQUARE and the CUBE
and then
This article is about mathematics. For mass media, see Political media.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So:
n4 = n × n × n × n
Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.
The sequence of fourth powers of integers (also known as biquadratic numbers or tesseractic numbers) is:
1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, ... (sequence A000583 in OEIS)
The last two digits of a fourth power of an integer can be easily shown (for instance, by computing the squares of possible last two digits of square numbers) to be restricted to only twelve possibilities:
00, 01, 16, 21, 25, 36, 41, 56, 61, 76, 81, 96
Every positive integer can be expressed as the sum of at most 19 fourth powers; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers (see Waring's problem).
Euler conjectured a fourth power cannot be written as the sum of 3 smaller fourth powers, but 200 years later this was disproven with:
958004 + 2175194 + 4145604 = 4224814.
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