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Old 2021-09-24, 06:10   #58
ATH
Einyen
 
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Dec 2003
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If n=p (mod p*ord(p)) then p*ord(p) < n even when p > sqrt(n), which I find a bit strange.

For example from the 2-spsp list:
6589845341971 = 485131 * 13583641

ord(13583641) = 485130 and 485130*13583641 = 6589831758330 < 6589845341971

But ord(13583641) could have easily been bigger, because often ord(p) = p-1, but I guess every time p>sqrt(n) then ord(p) < p-1, I guess that is why they are 2-spsp ?

Edit:
Here is a more extreme example:
137438953471 = 223 * 616318177

ord(616318177) = 37 << p-1

Last fiddled with by ATH on 2021-09-24 at 06:33
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