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Abstract Algebra

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Existence of Solutions to Multiple Congruences

ABSALG-AGOGVP

Which of the following simultaneous congruences does not have a solution?

A

$n \equiv 0 \pmod{4}, n \equiv 0 \pmod{12}, n \equiv 0 \pmod{15}$

B

$n \equiv 1 \pmod{4}, n \equiv 2 \pmod{12}$

C

$n \equiv 1 \pmod{12}, n \equiv 3 \pmod{29}$

D

All of the above have at least one solution.