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In number theory, a Wall–Sun–Sun prime or Fibonacci–Wieferich prime is a certain kind of prime number which is conjectured to exist, although none are known. == Definition == A prime ''p'' ≠ 2, 5 is called a Wall–Sun–Sun prime if ''p''2 divides the Fibonacci number , where the Legendre symbol has the values : Equivalently, a prime ''p'' is a Wall–Sun–Sun prime iff ''Lp'' ≡ 1 (mod ''p''2), where ''Lp'' is the ''p''-th Lucas number. A ''k''-Wall-Sun-Sun prime is defined as a prime ''p'' such that ''p''2 divides the ''k''-Fibonacci number (a Lucas sequence ''Un'' with (P, Q) = (''k'', -1)) , where is the Legendre symbol. For example, 241 is a ''k''-Wall-Sun-Sun prime for ''k'' = 3. Thus, a prime ''p'' is a ''k''-Wall-Sun-Sun prime iff ''Vk(p)'' ≡ 1 (mod ''p''2), where ''Vn'' is a Lucas sequence with (P, Q) = (''k'', -1). Least ''n''-Wall-Sun-Sun prime are :13, 241, 2, 3, 191, 5, 2, 3, 2683, ... (start with ''n'' = 2) 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「Wall–Sun–Sun prime」の詳細全文を読む スポンサード リンク
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