Mathematics I / Modular Arithmetic
Practice question · True or false

A congruence may be divided through by a factor only when that factor is coprime to the modulus.

Hints
  1. Try dividing 62(mod4)6 \equiv 2 \pmod 4 by 2.
  2. Coprimality is exactly the condition.
Show the answer

True

Why

True. 62(mod4)6 \equiv 2 \pmod 4 divided by 2 gives the false 31(mod4)3 \equiv 1 \pmod 4, because 2 shares a factor with the modulus. Where the factor is coprime the division is valid; otherwise the modulus must be divided too, giving 31(mod2)3 \equiv 1 \pmod 2.

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