Another kind of sequence puzzle

[Leroy Quet]

------=_Part_114770_16554780.1183484165194
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

Yes Joshua:
The only exception ocurrs if r | c or if c | r in the case abs(r-c)=prime;
in other words if r and c are multiples of p.


2007/7/2, Joshua Zucker <joshua.zucker at gmail.com>:
>
> Proof: if r and c are not coprime, then they have a common divisor d,
> and then d divides r+c and r-c as well.
>
> The only possible exceptions would be cases like 6 and 3, where 6-3 is
> prime even though 6 and 3 are not coprime.  That is, where the common
> divisor is a prime equal to r-c.
>
> --Joshua Zucker
>
>
> On 7/2/07, xordan <xordan.tom at gmail.com> wrote:
> > I understand that the attached file and the folloging words that  don't
> > coincide with the strict discussion line in seqfan, but they contain
> some
> > graphic curiosities that I wanted to share with the members of the list.
> I
> > wait some benevolent comments. Again I notice that the translation of
> the
> > original in Spanish is made with the help of software:
> >
> > The attached file (coprimes.zip ) contains one book of calculation
> sheets
> > that has 5 work sheets that give results (to my view) interesting
> related
> > with the numbers relatively primes.
> > The first sheet shows the numbers (1 to 256) relatively primes to each
> other
> >  that added (arithmetic sum)   becomes  a prime number as  result; the
> > second sheet shows the numbers relatively primes  whose absolute
> difference
> > becomes a prime number  as  result; the third are the conjunction of the
> > previous two , that is to say the numbers relatively primes  whose their
> > algebraic sum  gives as  result a prime  number. The fourth is the same
> > graph that it appears in the current page
> > http://mathworld.wolfram.com/RelativelyPrime.html
> > (RelativelyPrime.gif) and that it shows the primes numbers relatively to
> > each other. The fifth work sheet is the conjunction of
> RelativelyPrime.gif
> > and the previous sheet "abs(r+-c)=prime". - With this it is shown
> > graphically that all the numbers (r,c) whose algebraic sum is a prime
> number
> > (p) they are relatively prime to each other.
> > IF  r+c=p  THEN   coprime(r,c)=1.-
> > --
> > xordan at hotmail.com
> > xordan_co at yahoo.com
> > xordan.tom at gmail.com
> >
>



-- 
xordan at hotmail.com
xordan_co at yahoo.com
xordan.tom at gmail.com

------=_Part_114770_16554780.1183484165194
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

<div>Yes Joshua:</div>
<div>The only exception ocurrs if r | c or if c | r in the case abs(r-c)=prime; in other words if r and c are multiples of p. </div>
<div> <br> </div>
<div><span class="gmail_quote">2007/7/2, Joshua Zucker <<a href="mailto:joshua.zucker at gmail.com">joshua.zucker at gmail.com</a>>:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Proof: if r and c are not coprime, then they have a common divisor d,<br>and then d divides r+c and r-c as well.
<br><br>The only possible exceptions would be cases like 6 and 3, where 6-3 is<br>prime even though 6 and 3 are not coprime.  That is, where the common<br>divisor is a prime equal to r-c.<br><br>--Joshua Zucker<br><br><br>
On 7/2/07, xordan <<a href="mailto:xordan.tom at gmail.com">xordan.tom at gmail.com</a>> wrote:<br>> I understand that the attached file and the folloging words that  don't<br>> coincide with the strict discussion line in seqfan, but they contain some
<br>> graphic curiosities that I wanted to share with the members of the list. I<br>> wait some benevolent comments. Again I notice that the translation of the<br>> original in Spanish is made with the help of software:
<br>><br>> The attached file (coprimes.zip ) contains one book of calculation sheets<br>> that has 5 work sheets that give results (to my view) interesting related<br>> with the numbers relatively primes.<br>> The first sheet shows the numbers (1 to 256) relatively primes to each other
<br>>  that added (arithmetic sum)   becomes  a prime number as  result; the<br>> second sheet shows the numbers relatively primes  whose absolute difference<br>> becomes a prime number  as  result; the third are the conjunction of the
<br>> previous two , that is to say the numbers relatively primes  whose their<br>> algebraic sum  gives as  result a prime  number. The fourth is the same<br>> graph that it appears in the current page<br>> <a href="http://mathworld.wolfram.com/RelativelyPrime.html">
http://mathworld.wolfram.com/RelativelyPrime.html</a><br>> (RelativelyPrime.gif) and that it shows the primes numbers relatively to<br>> each other. The fifth work sheet is the conjunction of RelativelyPrime.gif<br>
> and the previous sheet "abs(r+-c)=prime". - With this it is shown<br>> graphically that all the numbers (r,c) whose algebraic sum is a prime number<br>> (p) they are relatively prime to each other.<br>
> IF  r+c=p  THEN   coprime(r,c)=1.-<br>> --<br>> <a href="mailto:xordan at hotmail.com">xordan at hotmail.com</a><br>> <a href="mailto:xordan_co at yahoo.com">xordan_co at yahoo.com</a><br>> <a href="mailto:xordan.tom at gmail.com">
xordan.tom at gmail.com</a><br>><br></blockquote></div><br><br clear="all"><br>-- <br><a href="mailto:xordan at hotmail.com">xordan at hotmail.com</a><br><a href="mailto:xordan_co at yahoo.com">xordan_co at yahoo.com</a><br><a href="mailto:xordan.tom at gmail.com">
xordan.tom at gmail.com</a> 

------=_Part_114770_16554780.1183484165194--



Are other people also having problems receiving the automated reply when 
with this.)

I guess we will have to wait until Neil gets back from vacation to submit 
via this method.

Thanks,
Leroy Quet