IMO Shortlist 1984 problem 2
Dodao/la:
arhiva2. travnja 2012. Prove:
(a) There are infinitely many triples of positive integers
![m, n, p](/media/m/d/0/e/d0eeeed7d9b201cd22dd9986bf6e1563.png)
such that
![4mn - m- n = p^2 - 1.](/media/m/c/9/9/c9909c9f234b7aec2b1d3baf38e4007e.png)
(b) There are no positive integers
![m, n, p](/media/m/d/0/e/d0eeeed7d9b201cd22dd9986bf6e1563.png)
such that
%V0
Prove:
(a) There are infinitely many triples of positive integers $m, n, p$ such that $4mn - m- n = p^2 - 1.$
(b) There are no positive integers $m, n, p$ such that $4mn - m- n = p^2.$
Izvor: Međunarodna matematička olimpijada, shortlist 1984