Can someone please explain how to do this problem?
Prove or disprove the statement “If $a \mid b$ and $c \mid d$, then $(a + c)\mid(b + d)$”.
Can someone please explain how to do this problem?
Prove or disprove the statement “If $a \mid b$ and $c \mid d$, then $(a + c)\mid(b + d)$”.
Take $a=2,b=4,c=3,d=3$, then what can you say ?
Hint $\ $ By the mediant inequality $\rm\:\frac{b}a < \frac{d}c\:\Rightarrow\:\frac{b}{a} < \frac{b+d}{a+c} < \frac{d}{c}.\:$ Therefore, when the extreme terms are consecutive integers, the middle term is not an integer.