Bhat, KG and Ramachandran, K (2010) Remark on factorials that are products of factorials. In: Mathematical Notes, 88 (3-4). pp. 317-320.
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In a paper published in 1993, Erdos proved that if n! = a! b!, where 1 < a a parts per thousand currency sign b, then the difference between n and b does not exceed 5 log log n for large enough n. In the present paper, we improve this upper bound to ((1 + epsilon)/ log 2) log log n and generalize it to the equation a (1)!a (2)! ... a (k) ! = n!. In a recent paper, F. Luca proved that n - b = 1 for large enough n provided that the ABC-hypothesis holds.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||factorial; product of factorials; Stirling's formula; prime factor|
|Date Deposited:||14 Dec 2010 10:17|
|Last Modified:||14 Dec 2010 10:17|
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