Difficult equation with three variables

[Guest]

Hello,

I thought up a math problem, and hope you all will find it interesting.

For positive integers a, b and c the following numbers are formed:

x = 60a + 13b and y = 60a + 11c

Now I have to find all possibilities of a, b and c to which the equation applies:

4 * [tex]x^{2}[/tex] - [tex]y^{2}[/tex] = 2020

and prove that there are no further solutions.

Thanks for all good answers

[Guest]

[tex]a = 4[/tex]
[tex]b = 1[/tex]
[tex]c = 24[/tex]

[tex]x = 60a + 13b = 60(4) + 13(1) = 253[/tex]
[tex]y = 60a + 11c = 60(4) + 11(24) = 504[/tex]

[tex]4 \cdot x^2 - y^2 = 4 \cdot (253)^2 - (504)^2 = 2020[/tex]


-Jambo