## A162290- third application

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• The Pomerance indices seem to have another application; we can find the minimum universal exponents pertaining to Carmichael numbers. For the present
Message 1 of 2 , Aug 1, 2009
The Pomerance indices seem to have another application; we can find
the minimum universal exponents pertaining to Carmichael numbers. For
the present I will just give one numerical illustration:

The Minimum u.e = (N-1)/2*(PI) where N = 3CN and PI is Pomerance
Index.

Take 561. Applying the above formula we get 2^(9+40*k) is congruent to
-49(mod(561)).

Here k belongs to N.

In pari this is {p(k)=if(Mod(2,561)^(9+40*k) + 49}

A.K. Devaraj

[Non-text portions of this message have been removed]
• To complete the pari ...,print( integer ). ... [Non-text portions of this message have been removed]
Message 2 of 2 , Aug 1, 2009
To complete the pari ...,print("integer").

> The Pomerance indices seem to have another application; we can find
> the minimum universal exponents pertaining to Carmichael numbers. For
> the present I will just give one numerical illustration:
>
> The Minimum u.e = (N-1)/2*(PI) where N = 3CN and PI is
> Pomerance Index.
>
> Take 561. Applying the above formula we get 2^(9+40*k) is congruent to
> -49(mod(561)).
>
> Here k belongs to N.
>
> In pari this is {p(k)=if(Mod(2,561)^(9+40*k) + 49}
>
> A.K. Devaraj
>

[Non-text portions of this message have been removed]
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