Monthly Archives: June 2015

Cyclic permutation of digits – GeometricMean[abc, bca] = cab

        Can you find other solutions?                               Advertisements

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Concatenation – Emirps

  An emirp is a prime number that results in a different prime when its digits are reversed. https://en.wikipedia.org/wiki/Emirp Let’s take all the emirps < 1000 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, … Continue reading

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Sequences of squares: a+1, ab+1, abc+1, abcd+1, …

  There exist an infinite number of infinite sequences of distinct positive integers    , … for which     , … are all squares.     then,     then,     then,     then,   etc.   … Continue reading

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Triangular numbers which are the sum of 7 consecutive squares

  The first few solutions:                                      

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Solutions to: Sum of 47 consecutive Squares is Square

                                   

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When Concatenations 13||N^2|| and 17||N^2||71 are prime

    Find     such that the concatenation (1)     is a prime number (2)     is a prime number     For all                           … Continue reading

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Triangular numbers that are sum of 11 consecutive squares

                                                           

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Solutions to: Sum of 33 consecutive Squares is Square

                                                                               

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Concatenation 11 || N^3 || 11 is a prime number (Part 2)

  Find     such that the concatenation     is a prime number For all                                  

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Solutions to: Sum of 11 consecutive Squares is Square

                                             

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