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Old 2022-09-23, 10:10   #1
enzocreti
 
Mar 2018

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Default 1666667*2 mod 666667

how do you see that

-1666667x2=1 mod 666667?

I simply tried but is there a method to "see" it?
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Old 2022-09-23, 14:22   #2
slandrum
 
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Quote:
Originally Posted by enzocreti View Post
how do you see that

-1666667x2=1 mod 666667?

I simply tried but is there a method to "see" it?
-1666667 = -333333 mod 666667 = 333334 mod 666667

is there more that you need to see?
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Old 2022-09-23, 17:39   #3
Dr Sardonicus
 
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A little algebra may help:

1666667 = (10^7 + 2)/6

666667 = (2*10^6 +1)/3

2*(10^7 + 2)/6 = (10^7 + 2)/3

(10^7 + 2)/3 = 5*(2*10^6 + 1)/3 - 1

2*(10^7 + 2)/6 == 1 mod (2*10^6 + 2)/3
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Periodicity of the congruence 1666667 mod 666667 enzocreti enzocreti 23 2018-12-02 16:26

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