Tag Archives: Cubes

{x+y, x^2+y^2, x^3+y^3} are squares, and {x^4+y^4} cubes

    Find two positive integers such that   Here’s one solution:         Find other solutions.                                           … Continue reading

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n-digit numbers whose cubes end with the same n digits

    1-digit :   =   64   =   216   =   729   2-digit :   =   13824   =   15625   =   117649   =   438976   3-digit :   = … Continue reading

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A^3 + B^3 = C^3 ± 1

                                                (1)                                                     ………………………………………………………………………. ……………………………………………………………………….   (2)                                                        …………………………………………………………………… …………………………………………………………………………                               … Continue reading

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Cubes with same digits

    The digits of can be permuted to form   cube whose digits can be permuted to produce two other cubes :               and three other cubes :     Paul found:   … Continue reading

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Cubes that begin with 2000,2001,…,2015

  Determine the smallest cubes that begin with,   2000,   2001,   2002,   …, 2015,   and the last digit (in each case) are from   0 to 9.   Here are some examples.   Complete the tables. … Continue reading

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Equation (A^3 + B^3)(C^3 – D^3) = N^3

      Here are some solutions:           Other sequences:     Find more solutions                        

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When is the sum of two squares a cube?

      multiplying both sides by                            

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Squares that can be transformed into a cube if two digits are increased by one

    excluding   ,   ,   etc.    excluding   ,     etc        Contributor:   pipo                        

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Squares that can be transformed into a cube if one digit is increased by 1

    Paul found: 39204   =   198^2 39304   =   34^3 39204000000   =   198000^2 39304000000   =   3400^3 98831640625   =   314375^2 98931640625   =   4625^3     pipo found: 1199462890625   … Continue reading

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(10*a + b) * c = a^2 + b^2 + c^2

      Paul found – Part 1   Pattern #2 :                    

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