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Fifth power factor (Posted on 2012-08-22) Difficulty: 3 of 5
Let n be a positive integer > 1, such that n5+5 and (n+1) 5+5 have a positive common factor, m. Find the possible values of m.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: computer exploration Comment 3 of 3 |
(In reply to computer exploration by Charlie)

Yes, because the periods are:

n = 1968751k+96502 
n = 1968751k+533360  
n = 1968751k+533361 
n = 1968751k+1066696 
n = 1968751k+1707583  

and 533361= 533360+1. So my 'Tricks alert!' antenna were working after all.

Incidentally, 61031281=1968751*31 has no less than 25 such periods, although none are consecutive.

  Posted by broll on 2012-08-23 01:39:47
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