Monthly Archives: September 2015

Equation : x^2 ± k*y^2 are square numbers, for k = 45 and 54

  (1)    k = 45     First few primitive solutions :         (2)    k = 54     First few primitive solutions :                       … Continue reading

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Equation : x^2 ± 80*y^2 are square numbers

    First few primitive solutions :                                            

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Equation : x^2 ± 28*y^2 are square numbers

    First few primitive solutions :                                          

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Equation : x^2 ± 20*y^2 are square numbers

    First few Primitive solutions :                                          

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Equation : x^2 ± 55*y^2 are square numbers

    First few primitive solutions :     other values for     and     such that                                        

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Equation : (x + m)^3 = n*x

    Consider,        ……….   (1) where     and     are positive integers, and the equation (1) has exactly three distinct integer solutions in   .   Let’s take, for example,   possible solutions:   , … Continue reading

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Equation : x^2 ± 84*y^2 are square numbers

                                     

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Equation : x^2 ± k*y^2 are square numbers, for k = 102, 120

  David found :     Here are few more primitive solutions:                                  

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Equation : x^2 ± k*y^2 are square numbers, for k = 125, 126

  David found :                                    

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Equation : x^2 ± k*y^2 are square numbers, for k = 111, 112

  David found:                                    

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