Monthly Archives: January 2017

Set {a,b,c,d,e} such that the product of any two of them increased by 1 is a square

    The set     has the property that the product of any two of them plus one is the square of a rational number. where         the next solutions are:   Find the next set. … Continue reading

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Set {a,b,c,d} such that the product of any two of them increased by 1 is a square — Part 3

      ………………….     ………………….     ………………….       ……………………     ……………………     ………..     Or     ……………………     ……………………     ………..                                      …………………………………………………………..           … Continue reading

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Set {a,b,c,d} such that the product of any two of them increased by 1 is a square — Part 2

      …………………     …………………     …………………     We set       ………………………     ………………………     …………………….                                 … Continue reading

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Set {a,b,c,d} such that the product of any two of them increased by 1 is a square — Part 1

      ………..     ………..     ………..     In part 1,   we set     ………………………………     ………………………     ………….                           … Continue reading

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A prime which is the reverse concatenation of the first n triangular numbers

    The sequence of triangular numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, …   631   is a prime number. 10631   … Continue reading

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Prime index of a palindromic hexagonal number

    A hexagonal number is a polygonal number of the form       is a 19-digital prime index of the 39-digital palindromic hexagonal number:                                  … Continue reading

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Prime that is sum of consecutive triangular numbers with prime indices — Part 2

  Prime that is sum of consecutive triangular numbers with prime indices — Part 1   Paul asks: If we consider the Index numbers 29 and 43, both prime and sum the consecutive triangular numbers with those prime indices the … Continue reading

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13331 expressible as a sum of the squares of three consecutive odd triangular numbers

    The odd triangular numbers are given by :   1, 3, 15, 21, 45, 55, 91, 105, 153, 171, 231, 253, 325, 351, 435, 465, 561, 595, 703, 741, 861, 903, 1035, 1081, 1225, 1275, 1431, 1485, 1653, … Continue reading

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Num3er 1258723

    A Pentagonal number is a polygonal number of the form     is a prime number.     is also prime index of a 13-digital palindromic pentagonal number                     … Continue reading

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Prime that is sum of consecutive triangular numbers with prime indices — Part 1

      then,   is a prime number.   is the smallest prime that is sum of the first consecutive triangular numbers with prime indices.                             … Continue reading

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