planetmath.org - Comments for "Carmichal number 561"
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Comments for "Carmichal number 561"enFallout of amateur research
http://planetmath.org/comment/19923#comment-19923
<a id="comment-19923"></a>
<p><em>In reply to <a href="http://planetmath.org/carmichalnumber561">Carmichal number 561</a></em></p>
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<p id="p1.1" class="ltx_p">We can use pari to find the smallest divisor of phi(n) for which
a congruence holds good. Example: consider the pseudoprime 341.
This is pseudo to the base 2. To find d, the smallest divisor
we run the program p(n) = (2^n -1)/341. It was found that
when n = 10, the function is exactly divisible by 341. Application:
When the program p(n) = (2^n+97)/341 was run for n = 1,10, no divisibility
was found. Hence 2^n + 97 is not divisible for any value of n.
However (2^n + 1007) is divisible by 341 before the program reaches
10. Similarly 40 is the smallest divisor of phi(561) ( 561 is
a Carmichael number). Hence any relevant program pertaining to
an exponential expression has to be run only till n reaches 40.</p>
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</ul>Tue, 04 Aug 2015 04:39:27 +0000akdevarajcomment 19923 at http://planetmath.org