58 lines
1.0 KiB
Python
58 lines
1.0 KiB
Python
from math import gcd
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from lib_prime import primes
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from lib_misc import modinv
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def find_m(p: int) -> int:
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rs = []
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test_n = p * 1337
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for m in range(1, p):
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test_f = f(test_n, m)
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if test_f % p == 0:
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rs.append(m)
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assert len(rs) == 1
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return rs[0]
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def calc_m(p: int) -> int:
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"""
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(n // 10 + (n % 10) * m) % p == 0
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a + b * m == 0 (mod p)
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b * m == -a (mod p)
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m == -a * b**-1 (mod p)
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"""
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n = p * 1337
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a = n // 10
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b = (n % 10)
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m = -a * modinv(b, p)
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m %= p
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return m
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def f(n: int, m: int = 34) -> int:
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left = n // 10
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right = n % 10 * m
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r = left + right
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return r
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def euler_274():
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ps = primes(10**7)
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sum_m = 0
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for p in ps:
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if gcd(p, 10) != 1:
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continue
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m = calc_m(p)
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if p < 1000:
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m_naiv = find_m(p)
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assert m == m_naiv
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sum_m += m
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return sum_m
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if __name__ == "__main__":
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solution = euler_274()
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print(f"e274.py: {solution}")
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assert solution == 1601912348822
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