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 Post subject: Number Theory and Analysis (1)Posted: Tue, 13 Oct 2009 19:46:49 UTC
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(Taken from the Pi Mu Epsilon Journal's Fall 2009 Problem Set)

The concatenation of integers, is defined as , and it does what you think it does.

i.e. likewise and

Find infinitely many triplets, such that

1) is NOT a palindrome
2) IS a palindrome.

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 Post subject: Posted: Fri, 23 Oct 2009 17:14:59 UTC
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Why can't it be p[10^LEN(q)] + q ?

LEN is LENgth function (in Basic anyway).

Is LEN(n) not "universal" ?

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 Post subject: Posted: Fri, 23 Oct 2009 18:31:12 UTC
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Denis wrote:
Why can't it be p[10^LEN(q)] + q ?

LEN is LENgth function (in Basic anyway).

Is LEN(n) not "universal" ?

I've never heard of it myself.

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 Post subject: Posted: Sat, 24 Oct 2009 01:33:43 UTC
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Well, it's actually ALEN(n) for number of digits;
LEN(n) is bit length.

ALEN(n) seems to be pretty well popular; Google it...

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 Post subject: Posted: Sat, 24 Oct 2009 02:19:09 UTC
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Denis wrote:
Well, it's actually ALEN(n) for number of digits;
LEN(n) is bit length.

ALEN(n) seems to be pretty well popular; Google it...

No thanks, I never really enjoy reading anything terribly computer science-y at least not coding-wise (algorithms are cool, but that's secretly number theory anyways). Thanks though!

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 Post subject: Re: Number Theory and Analysis (1)Posted: Sat, 24 Oct 2009 03:17:27 UTC
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Find infinitely many triplets, such that
1) is NOT a palindrome
2) IS a palindrome.

I fail to see why 1) is requested:
keep a=1 and c=2 (as example) and ALL resulting a||b||c will not be palindromes,
so infinite solutions; or did I miss something?

2) is sort of fun: first 2 lowest are (apart from trivials 000,111,444,999):
4^2||3^2||31^2 : 169961
96^2||1^2||127^2 : 9216116129

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 Post subject: Re: Number Theory and Analysis (1)Posted: Sat, 24 Oct 2009 03:24:57 UTC
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Denis wrote:
Find infinitely many triplets, such that
1) is NOT a palindrome
2) IS a palindrome.

I fail to see why 1) is requested:
keep a=1 and c=2 (as example) and ALL resulting a||b||c will not be palindromes,
so infinite solutions; or did I miss something?

2) is sort of fun: first 2 lowest are (apart from trivials 000,111,444,999):
4^2||3^2||31^2 : 169961
96^2||1^2||127^2 : 9216116129

You want both (1) and (2) true at the same time...

Nice problem!

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