1666667*2 mod 666667

enzocreti · 2022-09-23, 10:10

how do you see that

-1666667x2=1 mod 666667?

I simply tried but is there a method to "see" it?

slandrum · 2022-09-23, 14:22

Quote:

Originally Posted by enzocreti

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?

Dr Sardonicus · 2022-09-23, 17:39

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

2022-09-23, 10:10	#1
enzocreti Mar 2018 7²·11 Posts	*16666672 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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2022-09-23, 17:39	#3
Dr Sardonicus Feb 2017 Nowhere 1100001001110₂ Posts	A little algebra may help: 1666667 = (10^7 + 2)/6 666667 = (210^6 +1)/3 2(10^7 + 2)/6 = (10^7 + 2)/3 (10^7 + 2)/3 = 5(210^6 + 1)/3 - 1 2(10^7 + 2)/6 == 1 mod (210^6 + 2)/3