[seqfan] Re: a Diophantine equation

Jack Brennen jb at brennen.net
Wed Nov 12 03:14:58 CET 2008


I find the following additional solutions:

n a b
-----
8 112 180
9 336 540
10 1050 1728
12 11880 20160
13 4212 739200
13 49896 62400
15 242550 2695680
16 970200 10782720
17 12117600 14676480
18 3810240 840153600
18 35642880 89812800
22 18661104000 30116136960



David Newman wrote:
> A student,  named Daniel Reichman, asked this question.
> 
> Suppose that a,b, and c, integers, satisfy
> 
> a^2+b^2= c^2.
> 
> For which n are there a,b such that 2ab=n!  ?
> 
> He notes that there are at least three solutions:
> 
> For n=4, a=4, b=3
> For n=5  a=12, b=5
> For n=6, a=40, b=9
> 
> Are there any other such n?
> 
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> 
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> 
> 





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