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Unformatted text preview: 2 i mod 19 . I = 3 1 mod 19 = 3 I 1 = 3 2 mod 19 = I Â· I mod 19 = 9 I 2 = 3 4 mod 19 = I 1 Â· I 1 mod 19 = 5 I 3 = 3 8 mod 19 = I 2 Â· I 2 mod 19 = 6 I 4 = 3 16 mod 19 = I 3 Â· I 3 mod 19 = 17 I 5 = 3 32 mod 19 = I 4 Â· I 4 mod 19 = 4 3 50 = 3 32 Â· 3 16 Â· 3 2 Evaluate 3 50 mod 19 . This can be solved by repeated squaring. Set I i = 3 2 i mod 19 . I = 3 1 mod 19 = 3 I 1 = 3 2 mod 19 = I Â· I mod 19 = 9 I 2 = 3 4 mod 19 = I 1 Â· I 1 mod 19 = 5 I 3 = 3 8 mod 19 = I 2 Â· I 2 mod 19 = 6 I 4 = 3 16 mod 19 = I 3 Â· I 3 mod 19 = 17 I 5 = 3 32 mod 19 = I 4 Â· I 4 mod 19 = 4 3 50 mod 19 = I 5 Â· I 4 Â· I 1 mod 19 = 4 Â· 17 Â· 9 mod 19 = 4...
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 Spring '10
 M.J.Golin
 Computer Science, D. E. Marsh, Modular exponentiation

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