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I want to find the plain text from two cyphertexts of RSA, encrypted with two diffrent public keys. I know that: for E((n,e),m) = c0 and E((n,f),m) = c1 , c0^x . c1^y mod n = m mod n = m (ex + fy=1) But for some examples x (or y) is negative. I am trying to find the m for E((493,3),m) = 293 and E((493,5),m) = 421 I found that 3.2 + 5.(-1) = 1 so x = 2 and y = -1. But 293^1 . (421)^-2 mod n is not even an integer. What is my mistake here?

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    $\begingroup$ HINT: First compute the multiplicative inverse of 421 mod 493 using the extended Euclidean algorithm. $\endgroup$
    – Daniel S
    Dec 15, 2023 at 22:33

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