Prove or disprove: For all integers a, b, c, d, if a|b and c|d, then $$( a + c ) \mid ( b + d )$$

Name: Prove or disprove: For all integers a, b, c, d, if a|b and c|d, then \[( a + c ) \mid ( b + d )\]
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Question

Quizplus · Accepted Answer

The statement is false because the divisibility of sums does not necessarily follow from the divisibility of individual terms. Counterexample: Let a = 2, b = 4, c = 3, d = 6. Here, a|b and c|d, but (a+c) = 5 does not divide (b+d) = 10.

Prove or Disprove: for All Integers A, B, C, D (a+c)∣(b+d)( a + c ) \mid ( b + d )(a+c)∣(b+d)

Prove or Disprove: for All Integers A, B, C, D $( a + c ) \mid ( b + d )$