Question

How many pairs of integers are there such that \[\huge a^2+3b^2\] and \[\huge b^2+3a^2\] are perfect squares?

Answer 1

i proved both of them to even or odd

Answer 2

@satellite73 ?? @Callisto ??? @shadowfiend ?? @ParthKohli ??@Directrix ??

Answer 3

Brilliant.org?

Answer 4

I've seen such a problem, except the 3 was a 6.

Answer 5

\[a=b\]@shubhamsrg ;-)

Answer 6

http://openstudy.com/users/shubhamsrg#/updates/51582b72e4b0507ceba20312
:P

Answer 7

shouldn't there be infinite solutions for this?
when a=b
we have 4a^2

for various values of a(or b), this is always a perfect square! :O

Answer 8

no there are not infinite solutions!

Answer 9

where am I going wrong in my reasoning ?

Answer 10

1,1 can be a solution by hit and trial!