Euler problems/131 to 140
From HaskellWiki
| Line 4: | Line 4: | ||
Solution: | Solution: | ||
<haskell> | <haskell> | ||
| - | problem_131 = | + | primes=sieve [2..] |
| + | sieve (x:xs)=x:sieve [y|y<-xs,mod y x>0] | ||
| + | primeFactors n = factor n primes | ||
| + | where | ||
| + | factor _ [] = [] | ||
| + | factor m (p:ps) | p*p > m = [m] | ||
| + | | m `mod` p == 0 = p : factor (m `div` p) (p:ps) | ||
| + | | otherwise = factor m ps | ||
| + | |||
| + | isPrime n = case (primeFactors n) of | ||
| + | (_:_:_) -> False | ||
| + | _ -> True | ||
| + | problem_131 = | ||
| + | length $ takeWhile (<1000000) | ||
| + | [x| | ||
| + | a<-[1 .. ], | ||
| + | let x=(3*a*(a+1)+1), | ||
| + | isPrime x] | ||
</haskell> | </haskell> | ||
Revision as of 09:04, 14 December 2007
Contents |
1 Problem 131
Determining primes, p, for which n3 + n2p is a perfect cube.
Solution:
primes=sieve [2..] sieve (x:xs)=x:sieve [y|y<-xs,mod y x>0] primeFactors n = factor n primes where factor _ [] = [] factor m (p:ps) | p*p > m = [m] | m `mod` p == 0 = p : factor (m `div` p) (p:ps) | otherwise = factor m ps isPrime n = case (primeFactors n) of (_:_:_) -> False _ -> True problem_131 = length $ takeWhile (<1000000) [x| a<-[1 .. ], let x=(3*a*(a+1)+1), isPrime x]
2 Problem 132
Determining the first forty prime factors of a very large repunit.
Solution:
problem_132 = undefined
3 Problem 133
Investigating which primes will never divide a repunit containing 10n digits.
Solution:
problem_133 = undefined
4 Problem 134
Finding the smallest positive integer related to any pair of consecutive primes.
Solution:
problem_134 = undefined
5 Problem 135
Determining the number of solutions of the equation x2 − y2 − z2 = n.
Solution:
import List primes :: [Integer] primes = 2 : filter ((==1) . length . primeFactors) [3,5..] primeFactors :: Integer -> [Integer] primeFactors n = factor n primes where factor _ [] = [] factor m (p:ps) | p*p > m = [m] | m `mod` p == 0 = p : factor (m `div` p) (p:ps) | otherwise = factor m ps isPrime :: Integer -> Bool isPrime 1 = False isPrime n = case (primeFactors n) of (_:_:_) -> False _ -> True fstfac x = [(head a ,length a)|a<-group$primeFactors x] fac [(x,y)]=[x^a|a<-[0..y]] fac (x:xs)=[a*b|a<-fac [x],b<-fac xs] factors x=fac$fstfac x fastfun x |mod x 4==3=[a|a<-factors x,a*a<3*x] |mod x 16==4=[a|let n=div x 4,a<-factors n,a*a<3*n] |mod x 16==12=[a|let n=div x 4,a<-factors n,a*a<3*n] |mod x 16==0=[a|let n=div x 16,a<-factors n,a*a<3*n] |otherwise=[] slowfun x =[a|a<-factors x,a*a<3*x,let b=div x a,mod (a+b) 4==0] problem_135 =[a|a<-[1..groups],(length$fastfun a)==10]
6 Problem 136
Discover when the equation x2 − y2 − z2 = n has a unique solution.
Solution:
-- fastfun in the problem 135 groups=1000000 pfast=[a|a<-[1..5000],(length$fastfun a)==1] pslow=[a|a<-[1..5000],(length$slowfun a)==1] -- find len pfast=len pslow+2 -- so sum file.log and +2 problem_136 b=[a|a<-[1+b*groups..groups*(b+1)],(length$fastfun a)==1] google num -- write file to change bignum to small num =if (num>49) then return() else do appendFile "file.log" ((show$length$problem_136 num) ++ "\n") google (num+1) main=google 0
7 Problem 137
Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers.
Solution:
problem_137 = undefined
8 Problem 138
Investigating isosceles triangle for which the height and base length differ by one.
Solution:
problem_138 = undefined
9 Problem 139
Finding Pythagorean triangles which allow the square on the hypotenuse square to be tiled.
Solution:
problem_139 = undefined
10 Problem 140
Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation.
Solution:
problem_140 = undefined
