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We say that x is the inverse of a, modulo n, if ax is congruent to...

  1. We say that x is the inverse of a, modulo n, if ax is congruent to 1 (mod n). Use this definition to find the inverse, modulo 13, of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Show by example that when the modulus is composite, that not every number has an inverse.

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