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least_divisor_function [2014/02/22 02:24]
nikolaj
least_divisor_function [2015/04/25 19:25]
nikolaj
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 ==== Function ==== ==== Function ====
  
-| @#FFBB00: $ \mathrm{ld}:​\mathbb N^+\to\{1\}\cup\mathrm{Prime\ number} ​ $ | +| @#FFBB00: definiendum ​| @#FFBB00: $ \mathrm{ld}:​\mathbb N^+\to\{1\}\cup\mathrm{Prime\ number} ​ $ | 
-| @#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]]
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