Here is a nice old school question. "Legendary" question

>>8795875
a=3
b=4
(a^2 + b^2)/(ab+1) = 25/13
>Show that this equation is the square of an integer.
???

let
a=1
b=1
(a^2 + b^2)/(ab+1) = 2/2 = 1
1^2=1

>>8795895
Square of an integer almost means 2^n so sub in a = 0 and b = 2 and u get 4 which is 2^2 aswell

>>8795935
Keep going

>>8795875
Looks like Vieta jumping might work.

>>8795937
what???

(a^2+b^2)/(ab+1) is not always the square of an integer, so the question of the OP is retarded, and false.

>>8796023

Wikipedia Vieta jumping

>>8796023
>>8795937
>>8796023
>>8795895
I found what OP means, he can't even copy a fucking question right, let alone find the solution.

Show that if a, b and n=(a^2+b^2)/(ab+1) are integers, then n is also the square of an integer.

>>8796024
no thanks, I'd rather derive it myself.

>>8795875
for the case b = a^3 we have
(a^2+b^2)/(ab+1) = (a^2+a^6)/(a^4+1) = a^2(1+a^4)/(1+a^4) = a^2
unfortunately this doesn't cover all cases

>>8796325
spoken like a true mathematician

>>8796325
kek