36 lines
882 B
Haskell
36 lines
882 B
Haskell
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#!/usr/bin/env stack
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{- stack script
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--resolver lts-13.24
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--install-ghc
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--package arithmoi
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-}
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{-
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Consider the fraction, n/d, where n and d are positive integers. If n<d and
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HCF(n,d)=1, it is called a reduced proper fraction.
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If we list the set of reduced proper fractions for d ≤ 8 in ascending order of
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size, we get:
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1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
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It can be seen that there are 21 elements in this set.
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How many elements would be contained in the set of reduced proper fractions for
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d ≤ 1,000,000?
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-}
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{-# LANGUAGE NoImplicitPrelude #-}
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import Protolude
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import Math.NumberTheory.Primes
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-- reducedProper :: Int -> [Int]
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reducedProper d = do
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let pf = map fst $ factorise d
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x <- [1..d]
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guard (some (\p -> x `rem` p == 0) pf)
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return x
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main :: IO ()
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main = do
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print $ reducedProper 8
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