Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
least_divisor_function [2014/03/21 11:11] 127.0.0.1 external edit |
least_divisor_function [2015/04/25 19:25] nikolaj |
||
|---|---|---|---|
| Line 5: | Line 5: | ||
| | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{ld}(n):=\mathrm{min}\left(\mathrm{divisors}(n)\right) $ | | | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{ld}(n):=\mathrm{min}\left(\mathrm{divisors}(n)\right) $ | | ||
| - | ==== Discussion ==== | + | ----- |
| === Code === | === Code === | ||
| + | == Haskell == | ||
| + | <code haskell> | ||
| + | divides :: Integral a => a -> a -> Bool | ||
| + | divides d n = rem n d == 0 | ||
| + | </code> | ||
| + | |||
| <code haskell> | <code haskell> | ||
| ld :: Integral a => a -> a | ld :: Integral a => a -> a | ||
| Line 15: | Line 21: | ||
| | k^2 > n = n | | k^2 > n = n | ||
| | otherwise = ldf (k+1) n | | otherwise = ldf (k+1) n | ||
| + | </code> | ||
| + | |||
| + | using [[Set of divisors function]]: | ||
| + | <code haskell> | ||
| + | divides :: Integral a => a -> a -> Bool | ||
| + | divides d n = rem n d == 0 | ||
| </code> | </code> | ||
| === Theorems === | === Theorems === | ||
| If $n$ isn't a prime, then $n$ divided by the //least// divisor is some number bigger than $\mathrm{ld}(n)$ and hence | If $n$ isn't a prime, then $n$ divided by the //least// divisor is some number bigger than $\mathrm{ld}(n)$ and hence | ||
| ^ $\mathrm{ld}(n)^2\le n$ ^ | ^ $\mathrm{ld}(n)^2\le n$ ^ | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Subset of === | === Subset of === | ||
| [[Surjective function]] | [[Surjective function]] | ||
