Question

If (a^2+b^2)/(ab+1) is an integer for positive integer a and b, then prove that it is always a perfect square.

Answer 1

if i take a and b both as 2, my result will be 8/5 which is not a perfect square!

Answer 2

i said if it is an integer

Answer 3

2 is an integer alright! :O

Answer 4

no the value 8/5 is not an integer

Answer 5

so only when the result is an integer, it always turns out to be a perfect square

Answer 6

ohhh like that.. wait lemme see!!!

Answer 7

SORRY MY BAD..>!!!

Answer 8

how much mathematics do you know? university maths?

Answer 9

well apparently not enough to solve this i guess :D

Answer 10

do you need a clue?

Answer 11

no wait lemme think!!!

Answer 12

ok

Answer 13

ok you have taken too long, the answer is using vieta jumping and a descent
:D