Prove or disprove: For all integers $$a , b , c \text {, if } a \mid ( b + c ) \text {, then } a \mid b \text { and } a \mid c \text {. }$$

Question

Quizplus · Accepted Answer

The statement is false because if $ a \mid (b + c) $, it does not necessarily mean that $ a \mid b $ and $ a \mid c $. For example, let $ a = 2 $, $ b = 3 $, and $ c = 1 $. Here, $ a \mid (b + c) $ since $ 2 \mid 4 $, but $ a \nmid b $ and $ a \nmid c $ since 2 does not divide 3 or 1.

Prove or Disprove: for All Integers a,b,c, if a∣(b+c), then a∣b and a∣c. a , b , c \text {, if } a \mid ( b + c ) \text {, then } a \mid b \text { and } a \mid c \text {. }a,b,c, if a∣(b+c), then a∣b and a∣c.

Prove or Disprove: for All Integers $a , b , c \text {, if } a \mid ( b + c ) \text {, then } a \mid b \text { and } a \mid c \text {. }$