# palindromic number

## Primary tabs

Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

### a note about 11| { }

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

### Re: a note about 11| { }

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

### Re: a note about 11| { }

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

### Re: a note about 11| { }

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

### Re: a note about 11| { }

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

### Re: a note about 11| { }

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