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Old 2020-09-20, 20:17   #2
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

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Quote:
Originally Posted by fivemack View Post
To find Machin-like formulae for pi, I want to find sets of N where N^2+1 has only small prime factors. Tangentially, it would be nice to have a proof that, for example, n=485298 is the largest number where n^2+1 has no prime factor greater than 53.
See: http://oeis.org/A185389 (somewhere there could be a longer computed list also).
This problem is solvable by https://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem using a Pell type equation, where on the right side there is a -1 not 1.
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