math/fermat_little_theorem: update proof statement#2641
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pikulet wants to merge 2 commits intoTheAlgorithms:masterfrom
pikulet:math-fermat-little-theorem
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math/fermat_little_theorem: update proof statement#2641pikulet wants to merge 2 commits intoTheAlgorithms:masterfrom pikulet:math-fermat-little-theorem
pikulet wants to merge 2 commits intoTheAlgorithms:masterfrom
pikulet:math-fermat-little-theorem
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pikulet
commented
Oct 2, 2020
| b = 10 | ||
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| # using binary exponentiation function, O(log(p)): | ||
| print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p) |
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This was the previous check done!
pikulet
commented
Oct 2, 2020
| @@ -1,12 +1,24 @@ | |||
| # Python program to show the usage of Fermat's little theorem in a division | |||
| # According to Fermat's little theorem, (a / b) mod p always equals | |||
| # a * (b ^ (p - 2)) mod p | |||
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This is the original definition the author was working with. It's very convoluted and a is unnecessary in this equation (appears once on both LHS and RHS)
kbakdev
approved these changes
Oct 22, 2020
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Please reopen this pull request once you commit the changes requested or make improvements on the code. If this is not the case and you need some help, feel free to seek help from our Gitter or ping one of the reviewers. Thank you for your contributions! |
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Describe your change:
From wikipedia, the definition of fermat little theorem is that a**p = a (mod p)
In the old code, the author checked if:
(a/b) == a * (b**(p-2)) (mod p)
This is a rather convoluted way of expressing the fermat little theorem, which only involves two params a and p in the first place. The equivalent transformation was to do b**2/a to the original LHS and RHS.
I have also added the demonstration code for the special case when a is not divisible by p, then:
a**(p-1) = 1 (mod p)
Checklist:
Fixes: #{$ISSUE_NO}.