Divisibility property in mathematics
Not what you're looking for?
One of the most often misunderstood concepts in math is divisibility. Divisibility is a different operation than division and the two are often confused.
The solution describes the seven key properties of divisibility and proves them mathematically to show the reader that they are true and why they are important.
The seven divisibility properties are as follows:
(a) a|0, a|a
(b) a|1 if and only if a = ±1
(c) if a|b and c|d, then ac|bd (for c?0)
(d) if a|b and b|c, then a|c (for b?0)
(e) (a|b and b|a) if and only if a = ±b
(f) if a|b and b?0, then |a|?|b|
(g) if a|b and a|c, then a|(bx+cy) for any integers x,y.
Purchase this Solution
Solution Summary
This solution explains divisibility property in number theory. It also explains the differences between division and divisibility. This solution also provides proofs for properties of divisibility.
Solution Preview
Prove all the parts of the divisibility theorem, giving the basic properties of divisibility. Namely, show that for any integers a,b,c,d, with a≠0:
(a) a|0, a|a
(b) a|1 if and only if a=±1
(c) if a|b and c|d, then ac|bd (for c≠0)
(d) if a|b and b|c, then a|c (for b≠0)
(e) (a|b and b|a) if and only if a=±b
(f) if a|b and b≠0, then |a|≤|b|
(g) if a|b and a|c, ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.