Tag Archives: Powers of 2

Powers of 2 and 3 as a sum of two powers

                  and so on.   and so on.   and so on.                                     Advertisements

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Triples (a, b, c); ab-c, bc-a, ca-b are all powers of 2

    Find triples     of positive integers for which     and are all powers of 2   For example,   (a, b, c)   =   (2, 2, 2),   (3, 2, 2),   (11, 6, 2),   … Continue reading

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Powers of 2 | (2+1)(2^2 + 1)(2^4 + 1)(2^8 + 1) … + 1

    Using powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, … as shown   we always end up getting 4.   Explain.           … Continue reading

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Find smallest integer n so that 2^(10*n) doesn’t begin with digit 1

  These results all begin with 1 :     Find the smallest positive integer     where     produces a number that does not begin with 1                                                                  ——————————————   Solution:   Don S. McDonald and … Continue reading

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Powers of 2 – divisibility

    Let     be positive integers.     and       ….     ……     ….     ……     ….     ……     …     …..     …     ….. … Continue reading

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Powers of 2 in terms of factorials

    Generalize this.                                    

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Are there any positive integers n such that the expansion of 2^n ends in n?

    n = 36   is the first from this list.   Any others?   @chappulian found   n = 736   and   n = 8736   @shahlock:   n = 48736 Dave Radcliffe: a(2) = 36,   … Continue reading

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2^(4*n+2) + 1, n = 1,2,3,…,15

        To be continued.                          

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Powers of 2 puzzle

    Let M be a positive integer. Rearranging the digits of M, we obtain the positive integer N. No leading zeros. Is it possible to have two different positive integer powers of 2 this way?         … Continue reading

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Puzzle| Powers of 2 that may be represented as x^2 + 7*y^2

                     

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