(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a, b < c, and d are positive integers, prove the following inferences.

1. a|b [itex] \wedge [/itex] c|d [itex]\rightarrow[/itex] ac|bd

2. a|b <=> ac|bc

2. Relevant equations

3. The attempt at a solution

1.

a|b = x, then b = ax

c|d = y, then d = cy

bd = axcy

thus ac|bd = ac|axcy, and ac|axcy = xy

therefore ac|bd = xy if a|b = x and c|d = y

2.

c|ac = a and c|bc = b

so c|(ac|bc) = a|b

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Number Theory Division

**Physics Forums | Science Articles, Homework Help, Discussion**