Euler problems/131 to 140

Problem 131

Determining primes, p, for which n3 + n2p is a perfect cube.

Solution:

problem_131 = undefined

Problem 132

Determining the first forty prime factors of a very large repunit.

Solution:

problem_132 = undefined

Problem 133

Investigating which primes will never divide a repunit containing 10n digits.

Solution:

problem_133 = undefined

Problem 134

Finding the smallest positive integer related to any pair of consecutive primes.

Solution:

problem_134 = undefined

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]

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]
-- write file to change bignum to small num
=if (num>49)
then return()
else do appendFile "file.log" ((show\$length\$problem_136 num)  ++ "\n")

Problem 137

Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers.

Solution:

problem_137 = undefined

Problem 138

Investigating isosceles triangle for which the height and base length differ by one.

Solution:

problem_138 = undefined

Problem 139

Finding Pythagorean triangles which allow the square on the hypotenuse square to be tiled.

Solution:

problem_139 = undefined

Problem 140

Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation.

Solution:

problem_140 = undefined