Tag Archives: Powers

n-digit integers which are also an n-th power

    Here are some examples:   1-digit:       2-digit:       3-digit:     4-digit:     5-digit:     6-digit:     7-digit:     8-digit:     9-digit:               10-digit:               11-digit:     12-digit:     13-digit:     14-digit:     15-digit: … Continue reading

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Powers & Sum Digits – Num3ers from 2 to 20 — Part 1

  Numbers from 2 to 20   –   Part 1                              

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x^a + y^b = z^c with 1/a + 1/b + 1/c < 1

    ……………..              with          ……………     …………..     ………….     …………     Find other examples.                                                                  ——————————————   we need multiples of 3 for the values of   … Continue reading

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Numbers such that concatenation of prime factors is a power

    For example,                                

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Powers consisting of n distinct digits, averaging n

    Could we have more than 6 distinct digits?                                  

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3-digit num3ers whose odd powers (1 to 19) end with the same num3er

  This is the list of all 3 digit numbers, powers 1 to 19                        

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Patterns | (x + y + z)^n – (x^n + y^n + z^n); n = 2,3,5,7

      in     exponents being the prime numbers   2, 3, 5, 7 :     Find out whether the pattern continues with   n = 11, 13                   … Continue reading

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Patterns | Integer N, N^2 = x^3 + y^3

    To Be Continued                  

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Factors of 3 * 2^n – 1, n=1,2,..,100

     

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k * 2^n ± 1

      Paul found:      

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