Loading ...
Sorry, an error occurred while loading the content.

Counter invited (generalised)

Expand Messages
  • Devaraj Kandadai
    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
    • 0 Attachment
      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]
    • Jack Brennen
      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
      • 0 Attachment
        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
        >
      • Jack Brennen
        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
        • 0 Attachment
          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
          >
        • David Broadhurst
          ... 73^2 + 351352020312 73^6 + 351352020312 are both 6-Carmichael numbers. David
          Message 4 of 4 , Jul 25, 2009
          • 0 Attachment
            --- In primenumbers@yahoogroups.com,
            Jack Brennen <jfb@...> wrote:

            > 7^1+1722
            > 7^7+1722

            73^2 + 351352020312
            73^6 + 351352020312

            are both 6-Carmichael numbers.

            David
          Your message has been successfully submitted and would be delivered to recipients shortly.