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In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if are coprime integers, then for any integer ''n'' ≥ 1, there is a prime number ''p'' (called a ''primitive prime divisor'') that divides and does not divide for any positive integer , with the following exceptions: *, ; then = 1 which has no prime divisors *, a power of two; then any odd prime factors of = must be contained in , which is also even *, , ; then = 63 = 3²7 = This generalizes Bang's theorem, which states that if and ''n'' is not equal to 6, then has a prime divisor not dividing any with . Similarly, has at least one primitive prime divisor with the exception . Zsigmondy's theorem is often useful, especially in group theory, where it is used to prove that various groups have distinct orders except when they are known to be the same. ==History== The theorem was discovered by Zsigmondy working in Vienna from 1894 until 1925. 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「Zsigmondy's theorem」の詳細全文を読む スポンサード リンク
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