## Counter invited (generalised)

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• A few days ago I had invited a counter to the following: 561 is the only Carmichael number generated by 2^n + 49.. This invitation can be generalised as
Message 1 of 4 , Jul 24, 2009
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A few days ago I had invited a counter to the following:

561 is the only Carmichael number generated by 2^n + 49..

This invitation can be generalised as follows:

a^n + c can, at the most , generate only one C.n. Here a,n & c
belong to N; n is the only variable.

Counter examples invited.

A.K. Devaraj

[Non-text portions of this message have been removed]
• You don t even need to look far... 73^1 + 10512 73^2 + 10512 Both are Carmichael numbers. Or another one easy to find: 273^1 + 832 273^2 + 832
Message 2 of 4 , Jul 24, 2009
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You don't even need to look far...

73^1 + 10512
73^2 + 10512

Both are Carmichael numbers.

Or another one easy to find:

273^1 + 832
273^2 + 832

> A few days ago I had invited a counter to the following:
>
> 561 is the only Carmichael number generated by 2^n + 49..
>
> This invitation can be generalised as follows:
>
> a^n + c can, at the most , generate only one C.n. Here a,n & c
> belong to N; n is the only variable.
>
> Counter examples invited.
>
> A.K. Devaraj
>
• Overlooked an even smaller one because I was only looking up to squares: 12^1+1093 12^3+1093 Here s an interesting one: 7^1+1722 7^7+1722
Message 3 of 4 , Jul 24, 2009
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Overlooked an even smaller one because I was only looking up to squares:

12^1+1093
12^3+1093

Here's an interesting one:

7^1+1722
7^7+1722

Jack Brennen wrote:
> You don't even need to look far...
>
> 73^1 + 10512
> 73^2 + 10512
>
> Both are Carmichael numbers.
>
> Or another one easy to find:
>
> 273^1 + 832
> 273^2 + 832
>
• ... 73^2 + 351352020312 73^6 + 351352020312 are both 6-Carmichael numbers. David
Message 4 of 4 , Jul 25, 2009
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