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Back to Multiplicative Inverses

Exercise 3

Avg difficulty 2.5

Solve the following congruences. If none exists, explain why. If there are one or more solutions, give a complete list of solution(s).

  1. 3x−4=15(mod26)3x - 4 = 15 \pmod{26}
  2. 13x−3=4(mod26)13 x - 3 = 4 \pmod{26}
  3. 8x=16(mod426)8x=16\pmod{426}
  4. 8x=16(mod425)8x=16\pmod{425}
  5. 8x=21(mod426)8x=21\pmod{426}

Hammond, Discrete Math for Shockers, §3.4 Multiplicative Inverses, Exercise 3

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Adapted from Discrete Math for Shockers © 2021 John Hammond. Licensed under CC BY-SA 4.0. Source: Discrete Math for Shockers. Imported at revision 2538beb.