3 Congruence
Theorem 3.4 If a b mod n then a and b leave the same remainder when divided by n. Conversely if a and b leave the same remainder when divided by n, then a b mod n. Proof: Suppose a b mod n. Then by Theorem 3.3, b = a+nq.Ifa leaves the remainder r when divided by n,wehavea = nQ + r with 0 r<n. Therefore, b = a + nq =
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Numerical Methods I: Eigenvalues and eigenvectors
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