35 lines
828 B
Python
35 lines
828 B
Python
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import gmpy2
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from gmpy2 import mpz
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def sqrt_mod(b):
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p = mpz(7)
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b = mpz(b) % p
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if p % 4 != 3:
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raise ValueError("Liczba p musi spełniać p ≡ 3 mod 4.")
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legendre_symbol = gmpy2.powmod(b, (p - 1) // 2, p)
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if legendre_symbol != 1:
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raise ValueError(f"{b} nie jest resztą kwadratową modulo {p}.")
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exponent = (p + 1) // 4
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a = gmpy2.powmod(b, exponent, p)
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if (a * a) % p != b:
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raise ValueError("Nie udało się znaleźć pierwiastka kwadratowego.")
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return a
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b_input = input("Podaj wartość b: ")
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try:
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b = mpz(b_input)
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except ValueError:
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print("Błędne dane: b musi być liczbą całkowitą.")
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exit()
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try:
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wynik = sqrt_mod(b)
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print(f"Pierwiastek kwadratowy z {b} modulo 7 to {wynik}.")
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except ValueError as e:
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print(e)
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