41 lines
1.2 KiB
Python
41 lines
1.2 KiB
Python
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def fib():
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a, b = 1, 1
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yield a
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yield b
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while True:
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a, b = b, a + b
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yield b
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def pisano_period(fibs, n):
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for period in range(2, 130):
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if fibs[0] % n == fibs[period] % n and fibs[1] % n == fibs[period + 1] % n:
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return period
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return None
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def euler_853():
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r = 0
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fs = fib()
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fibs = [next(fs) for _ in range(400)]
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upper = 10**9
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pi_target = 120
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for n in range(2, upper + 1):
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# Check if pi_target is a period.
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if fibs[0] % n == fibs[pi_target] % n and fibs[1] % n == fibs[pi_target + 1] % n:
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# Make sure that no lower period than pi_target exits.
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if pisano_period(fibs, n) == pi_target:
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r += n
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# print(n, prime_factors(n))
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# I have noticed that the highest prime factor is always 61 or
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# 2521, so we could probably also get the solution by
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# enumerating the prime factors that yield a sum smaller than
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# upper and have 61 or 2521 as their last factor.
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return r
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if __name__ == "__main__":
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solution = euler_853()
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print("e853.py: " + str(solution))
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assert solution == 44511058204
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