Brocard's problem
The Diophantine problem of finding an integer, whose factorial plus one is a perfect square
Nº Q1052622 ★★★
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Brocard's problem
The Diophantine problem of finding an integer, whose factorial plus one is a perfect square
Brocard's problem is a problem in mathematics that seeks integer values of n {\displaystyle n} such that n ! + 1 {\displaystyle n!+1} is a perfect square, where n ! {\displaystyle n!} is the factorial. Only three values of n {\displaystyle n} are known — 4, 5, 7 — and it is not known whether there are any more.
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From Wikipedia
Brocard's problem is a problem in mathematics that seeks integer values of n {\displaystyle n} such that n ! + 1 {\displaystyle n!+1} is a perfect square, where n ! {\displaystyle n!} is the factorial. Only three values of n {\displaystyle n} are known — 4, 5, 7 — and it is not known whether there are any more. Though research has extended far beyond n > 7, no additional solutions to the equation n! + 1 = m2 are known. More formally, it seeks pairs of integers n {\displaystyle n} and m {\displaystyle m} such that n ! + 1 = m 2 . {\displaystyle n!+1=m^{2}.} The problem was posed by Henri Brocard in a pair of articles in 1876 and 1885, and independently in 1913 by Srinivasa Ramanujan.
Text: Wikipédia, CC BY-SA 4.0. ·
