# Euler problems/181 to 190

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< Euler problems(Difference between revisions)

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-- The expression (round $ fromIntegral n / e) computes the integer k | -- The expression (round $ fromIntegral n / e) computes the integer k | ||

− | -- for which (n/k)^k is at a maximum. | + | -- for which (n/k)^k is at a maximum. Also note that, given a rational number |

+ | -- r and a natural number k, the decimal expansion of r^k terminates if | ||

+ | -- and only if the decimal expansion of r does. | ||

answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n | answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n | ||

| n <- [5 .. 10^4]] | | n <- [5 .. 10^4]] |

## Revision as of 20:30, 24 February 2008

## 1 Problem 181

Investigating in how many ways objects of two different colours can be grouped.

Solution: This was my code, published here without my permission nor any attribution, shame on whoever put it here. Daniel.is.fischer

## 2 Problem 182

RSA encryption.

Solution:

fun a1 b1 = sum [ e | e <- [2..a*b-1], gcd e (a*b) == 1, gcd (e-1) a == 2, gcd (e-1) b == 2 ] where a=a1-1 b=b1-1 problem_182=fun 1009 3643

## 3 Problem 183

Maximum product of parts.

Solution:

-- Does the decimal expansion of p/q terminate? terminating p q = 1 == reduce [2,5] (q `div` gcd p q) where reduce [] n = n reduce (x:xs) n | n `mod` x == 0 = reduce (x:xs) (n `div` x) | otherwise = reduce xs n -- The expression (round $ fromIntegral n / e) computes the integer k -- for which (n/k)^k is at a maximum. Also note that, given a rational number -- r and a natural number k, the decimal expansion of r^k terminates if -- and only if the decimal expansion of r does. answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n | n <- [5 .. 10^4]] where e = exp 1 main = print answer