We consider the equation , where , , are positive integers.
Prove:
(a) There are no solutions for .
(b) For , must be divisible by for every solution .
(c) The equation has infinitely many solutions for .
We consider the equation $a^2 + b^2 + c^2 + n = abc$, where $a$, $b$, $c$ are positive integers.
Prove:
\\\\(a) There are no solutions $(a, b, c)$ for $n = 2017$.
\\\\(b) For $n = 2016$, $a$ must be divisible by $3$ for every solution $(a, b, c)$.
\\\\(c) The equation has infinitely many solutions $(a, b, c)$ for $n = 2016$.
Izvor: Srednjoeuropska matematička olimpijada 2016, ekipno natjecanje, problem 8
Školjka 
, where 
, 
, 
are positive integers.
for 
. 
, 
for every solution