## Except 11

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• Hi all; Can someone point me to a site with the proof for the following (I Googled till blue in the face because:) I dont know the English word for what in
Message 1 of 2 , Dec 8, 2006
Hi all;

Can someone point me to a site with the proof for the following (I
Googled till blue in the face because:) I dont know the English word
for what in Spanish is called a capicua (head-bum) number. 9889, 34543
etc.
Anyway, there appears to be some proof saying that if the number of
digits is equal (9889) it cannot be a prime except for 11. If its not
equal (34543) it can be.

To give a proof btw, was in a math exam for my then 9 years old son
when living in Spain.

Thanks,

Maarten
• ... I do like the idea of a head bum number! In English, it s rather less poetic - merely a palindrome . ... The simplest proof is probably to prove and use
Message 2 of 2 , Dec 8, 2006
--- maartenvanthiel <m.v.thiel@...> wrote:
> Hi all;
>
> Can someone point me to a site with the proof for the following (I
> Googled till blue in the face because:) I dont know the English word
> for what in Spanish is called a capicua (head-bum) number. 9889, 34543
> etc.

I do like the idea of a 'head bum' number! In English, it's rather less poetic
- merely a 'palindrome'.

> Anyway, there appears to be some proof saying that if the number of
> digits is equal (9889) it cannot be a prime except for 11. If its not
> equal (34543) it can be.
>
> To give a proof btw, was in a math exam for my then 9 years old son
> when living in Spain.

The simplest proof is probably to prove and use the alternating sum of digits
property which is often used to check for divisibility by 11.

Another would be proof that a number matching /1(00)*1/ is divisibly by 11, as
all even-lengthed palindromes are sums of such numbers.

Of course, it is the same underlying property that is being exploited by both.
(The fact that 10 == -1 (mod 11).)

Phil

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