Fork me on GitHub
Math for the people, by the people.

User login

palindromic number

Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

11A63 no label found

Comments

Let k,n denote positive integer numbers. It is easy to see that the sequences a_k=10^{2k-1}+1 and b_n=10^{2n}-1 are divisible by 11. Hence 11|a_k+b_n. From this, it is easy to prove that 11 divides every even length palindromic number.
perucho

Good point, but I'd prefer to generalize 11 to b + 1.

That's correct Wilfredo, but my note arose due to a suggestion that drini did to akrowne in his entry ``palindrome''. So now you can construct (if you want it) a general proof.
Cheers,
Pedro

Thanks.

So how do I create a link to the proof (the one about ELPNs)? It shows up as an attachment, but I'd like to link to it in the body text, too.

Wil

Thanks to you! It was your idea!
No problem; I already gave you full access to the entry and you can make the changes that you consider convenient.
Also, I have checked $(ELPN)_n$ (Eq.(6)) for a binary base and 6-length. So,
$b=2$, $n=3$. I took: $b_0=b_1=1$,$b_2=0$. By using $3=1.2^0+1.2^1=11$, I did the multiplication $10001x11$ and I got the Even Length Palindromic Number=$(ELPN)_3= 110011$. If you like you may add this example.
perucho

Thanks. I'll use that access carefully and judiciously. I'm at work right now but I'll be pondering your new example later.

Subscribe to Comments for "palindromic number"