Num3er 65

 
                                        Every number has a story to tell.  

 
That’s how I see it.

 
 

 
The factors of   65   are:     1     5     13     65

The prime factors are:        5 * 13

Sum of divisors:     84
 

   65^2   =   4225
(6+5)+2   =   4+2+2+5   =   13

   65^3   =   274625
2+7+4+6+2+5   =   26   =   2*13
 

65   +   56   =   121   =   11^2
65   –   56   =   9   =   3^2

 

                                                                                                     65^2 – 56^2   =   33^2
                                                                                          6165^2 – 6156^2   =   333^2
                                                                               617165^2 – 617156^2   =   3333^2
                                                                    61727165^2 – 61727156^2   =   33333^2
                                               617283827165^2 – 617283827156^2   =   3333333^2
                                   61728393827165^2 – 61728393827156^2   =   33333333^2
                        6172839493827165^2 – 6172839493827156^2   =   333333333^2
            617283950493827165^2 – 617283950493827156^2   =   3333333333^2
61728395060493827165^2 – 61728395060493827156^2   =   33333333333^2

 

65   =   2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11

65   =   1^5   +   2^4   +   3^3   +   4^2   +   5^1

65   =   1^2   +   8^2
65   =   4^2   +   7^2

65   =   (63^2   +   16^2)
65   =   (56^2   +   33^2)
 

         65   =   33^2   –   32^2
      665   =   333^2   –   332^2
   6665   =   3333^2   –   3332^2
66665   =   33333^2   –   33332^2

and so on.

            65^2   =   4225
         665^2   =   42225
      6665^2   =   44422225
   66665^2   =   444222225
666665^2   =   44442222225

and so on.
 

      65   =   1^3   +   4^3
65^2   =   1^3   +   4^3   +   4^3   +   16^3
 

65^4   =   64^4 + 32^4 + 12^4 + 8^4 + 1^4   =   52^4 + 46^4 + 39^4 + 2^4
 
 

65   base-10   =   1000001   base-2
65   base-10   =   2102   base-3
65   base-10   =   1001   base-4
65   base-10   =   230   base-5
65   base-10   =   145   base-6
65   base-10   =   122   base-7
65   base-10   =   101   base-8
65   base-10   =   72   base-9
65   base-10   =   55   base-12
65   base-10   =   50   base-13
65   base-10   =   49   base-14
65   base-10   =   45   base-15
65   base-10   =   41   base-16
65   base-10   =   38   base-19
65   base-10   =   35   base-20
65   base-10   =   32   base-21
65   base-10   =   29   base-28
65   base-10   =   27   base-29
65   base-10   =   25   base-30
65   base-10   =   23   base-31
65   base-10   =   21   base-32
65   base-10   =   19   base-56
65   base-10   =   18   base-57
65   base-10   =   17   base-58
65   base-10   =   16   base-59
65   base-10   =   15   base-60
65   base-10   =   14   base-61
65   base-10   =   13   base-62
65   base-10   =   12   base-63
65   base-10   =   11   base-64

Palindromic :
65   base-10   =   1000001   base-2
65   base-10   =   1001   base-4
65   base-10   =   101   base-8
65   base-10   =   55   base-12
65   base-10   =   11   base-64

Reversed digits :
65   base-10   =   230   base-5
65   base-10   =   32   base-21
65   base-10   =   72   base-9
65   base-10   =   27   base-29
65   base-10   =   41   base-16
65   base-10   =   14   base-61
65   base-10   =   32   base-21
65   base-10   =   23   base-31
65   base-10   =   21   base-32
65   base-10   =   12   base-63

 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty, Maths In The News and tagged , . Bookmark the permalink.

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