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In arithmetic and algebra, the fourth power of a number ''n'' is the result of multiplying four instances of ''n'' together. So: :''n''4 = ''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, 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: 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 (Elkies, Frye) with: 958004 + 2175194 + 4145604 = 4224814. That the equation ''x''4 + ''y''4 = ''z''4 has no solutions in nonzero integers (a special case of Fermat's Last Theorem), was known, see Fermat's right triangle theorem. ==Equations containing a fourth power== Fourth degree equations, which contain a fourth degree (but no higher) polynomial are, by the Abel-Ruffini theorem, the highest degree equations solvable using radicals. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fourth power」の詳細全文を読む スポンサード リンク
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