Proof of Divisibility of 8 rule

  • Thread starter Thread starter smiles988
  • Start date Start date
  • Tags Tags
    Divisibility Proof
smiles988
Messages
6
Reaction score
0

Homework Statement


Let n be a natural number. If the number formed by the last three digits of n is divisible by 8, then n is divisible by 8.


Homework Equations


Natural numbers are the set of {1,2,3,4,5,6,...}


The Attempt at a Solution


I believe we should use a direct proof to prove this conditional statement. Thus we will assume that n is a natural number and the number formed by the last three digits of n is divisible by 8. We will prove that n is divisible by 8.
I don't know where to go from here. Please help!
 
Physics news on Phys.org
Hint: What is the lowest power of 10 that is divisible by 8?
 
Reply to Hint

Okay so 1000 is the lowest power of 10 that is divisible by 8. How do I use that?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Base 8 Logic Puzzle: Finding Solutions to Divisibility Rules
Replies
9
Views
2K
Show That If Alt Sum of Digits Div By 11, n Is Divisible By 11
Replies
1
Views
2K
Prove True/False that n^3-n is Always Divisible By 6
Replies
4
Views
2K
Discrete Math Proof: Necessary Condition for Divisibility by 6
Replies
3
Views
4K
The only prime of the form n^3-1 is 7?
Replies
2
Views
4K
Prove every subset of countable set is either finite or else countable
Replies
1
Views
2K
Proof: Divisibility of Integers by 4
Replies
5
Views
2K
Proof That an Integer is Divisible by 2
Replies
3
Views
2K
Root test proof using Law of Algebra
Replies
6
Views
2K
Proving n^2 is Divisible by 4: Contradiction Method
Replies
13
Views
3K

Hot Threads

Recent Insights

Back
Top