# 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

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

First few primitive solutions :

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

First few primitive solutions :

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

First few Primitive solutions :

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

First few primitive solutions :     other values for     and     such that

## 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

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

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

David found :     Here are few more primitive solutions: