How do I prove that if the quotient of: (a^2 + b^2)/(ab+1) is

>(2^2+2^2)/(2*2+1)=8/5 is an integer

>>8282702
you go back to school and report underage posters

>>8282702
Let k =
a2 + b2ab + 1

We assume that there exist one or more solutions to the given condition for which k is not a perfect square.

For a given value of k, let (A, B) be the solution to this equation that minimizes the value of A + B and without loss of generality A ≥ B. We can rearrange the equation and replace A with a variable x to yield x2 – (kB)x + (B2 – k) = 0. One root of this equation is x1 = A. By Vieta's formulas, the other root may be written as follows:
x2 = kB – A = 1/A(B2 – k).

The first equation shows that x2 is an integer and the second shows that it is nonzero (if it were zero, k = B2, but we have assumed that k is not a perfect square). Also, x2 cannot be less than zero, because that would imply that –kBx2 ≥ k which implies that 0 = x22 – kBx2 + B2 − k ≥ x22 + B2 > 0 which is a contradiction. Finally, A ≥ B implies that
x2 = B2 − k/A < A which implies that x2 + B < A + B which contradicts the minimality of (A, B).

I think it is right.

>>8282707
>One possible set of numbers in place of a and b
>a=/=b
Look at the lib art major everyone

>>8282713
Thanks for that angle, I'm gonna ask my calc professor from last semester if that sounds right. I saw this problem from the 1986 Intl Math Olympics and it threw me off

>>8282707
Holy shit are you retarded???? If it is an integer, it is a square. 8/5 is not an """"""""""""integer""""""""""""""

>I just watched the latest reddit pop-math youtube video and now I want you to explain it to me
Fuck off and die, preferably in that order

>>8282724
>I saw this problem from the 1986 Intl Math Olympics and it threw me off
No you watched numberphile video you autistic child, google up a solution yourself

>>8282784
:^)

File: 20160819_223900.jpg (755KB, 1836x3264px) Image search: [Google]

755KB, 1836x3264px

Proof is in a section of a book I am reading by Geoff Smith.