41 lines
896 B
Python
41 lines
896 B
Python
from math import gcd
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from fractions import Fraction
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def product(xs):
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r = 1
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for x in xs:
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r *= x
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return r
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def ratio(d):
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r = 0
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for i in range(1, d):
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if gcd(i, d) == 1:
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r += 1
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return Fraction(r, (d - 1))
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def euler_243():
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target = Fraction(15499, 94744) # 0.1635881955585578
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# The more prime factors, the lower the initial fraction gets. We figure
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# out empirically that using primes up to 23 yields results close to the
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# target fraction. We then iterate over the multiples to find the
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# solution.
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factors = [2, 3, 5, 7, 11, 13, 17, 19, 23]
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for mul in range(1, 10):
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d = mul * product(factors)
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r = ratio(d)
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if r < target:
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return d
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return None
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if __name__ == "__main__":
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solution = euler_243()
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print("e243.py: " + str(solution))
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assert(solution == 892371480)
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