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The following table lists the powers of 3 modulo 31. 2 Powers of 3 modulo 31 i 3 3i i zii 3 3 3i 1

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The following table lists the powers of 3 modulo 31. 2 Powers of 3 modulo 31 i 3 3i i zii 3 3 3i 1 3 7 17 13 24 19 12 25 6 2 9 8 20 14 10 20 5 26 5 26 18 3 279 29 15 30 21 15 27 23 4 19 10 25 16 28 22 14 28 7 5 26 11 13 17 22 23 11 29 21 6 16 12 8 18 4 24 2 30 1 Find all numbers between 1 and 31 that have order 6 modulo 31. Solve the congruence x4 = 10 (mod 31)

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