- 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

Devaraj Kandadai wrote:> 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

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

> - --- In primenumbers@yahoogroups.com,

Jack Brennen <jfb@...> wrote:

> 7^1+1722

73^2 + 351352020312

> 7^7+1722

73^6 + 351352020312

are both 6-Carmichael numbers.

David