Modulo Q

Modulo Q. N(x + 1)), there are consecutive elements of order n modulo q. N(x + 1)), there are consecutive elements of order n modulo q.

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Many directions one could try to push this. Choose your encryption key to be at least 10. The modulo operation is the same as ' the remainder of the division '.

If q(x) = x3 + x + 3, we can just try all residues to see the only solution is x 1 (mod 5).

I.e., if there exists an integer x such that: Otherwise, the number r is the remainder of the division, where x is the dividend, and y is the divisor. Now suppose p 3 (mod 4). Then p 1 (mod q);

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Using ea and eea to solve inverse mod.

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Therefore we can nd two of the solutions and such that (mod p) and (mod q).

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For each of the following numbers, compute their residues modulo 12 (a) 129 (b) 340 (c) 31 (d) 5602 (e) 1000 (f) 120 3.

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Show all show all steps.

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().otherwise, q is called a quadratic nonresidue modulo n.

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Is true if such an integer q (called quotient) exists, then:

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When the remainder becomes 0, continue the calculation of x for one more round.

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We conclude that if we nd a prime q 1 (mod n) that divides res(n(x);

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If q(x) = x3 + x + 3, we can just try all residues to see the only solution is x 1 (mod 5).