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Abstract Algebra

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Values of Integral Linear Combinations

ABSALG-YECDE9

Which of the following numbers cannot be written as an integral linear combination of 27 and 45?

In other words, for which number $x$ does there exist no solution to the equation $27a+45b=x$, where $a$ and $b$ have to be integers?

A

$3$

B

$9$

C

$-27$

D

$45$

E

lcm$(27,45)$