Find all the solutions for k and L where both of them are positive integers and

3(2k+1)(2k-1)=L^2

Find all the solutions for k and L where both of them are positive integers and

3(2k+1)(2k-1)=L^2

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TopNewestHi;

It looks like a homework question and it appears that your book/teacher expects you to say that \[(k,L) = (1,3)\] is the only solution.

However, there are more solutions. The next solution is 141 digits.

To verify this, you'll need a Computer Algebra System or a multi-precision programming language.

Furthermore, I conjecture that there are infinite such solutions

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@Gaurav Sharma , I am sorry. {k -> 181, L -> 627}, {k -> 13, L -> 45} also works. There are many small solutions too.

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Thanks mahn !

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@Calvin Lin @Krishna Ar @Agnishom Chattopadhyay

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