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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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 – Agnishom Chattopadhyay · 2 years, 5 months ago

Log in to reply

@Gaurav Sharma , I am sorry. {k -> 181, L -> 627}, {k -> 13, L -> 45} also works. There are many small solutions too. – Agnishom Chattopadhyay · 2 years, 5 months ago

Log in to reply

– Gaurav Sharma · 2 years, 5 months ago

Thanks mahn !Log in to reply

@Calvin Lin @Krishna Ar @Agnishom Chattopadhyay – Gaurav Sharma · 2 years, 5 months ago

Log in to reply