x-y-z-are-positive-integers-find-all-solutions-of-x-2-y-2-1-xyz-

Question Number 56800 by mr W last updated on 24/Mar/19

x, y, z a r e p o s i t i v e i n t e g e r s .

f i n d a l l s o l u t i o n s o f x^{2} + y^{2} + 1 = x y z .

Commented by MJS last updated on 24/Mar/19

with z = 3 we get pairs of Fibonacci numbers

for (x, y) or (y, x) with each 2^{nd} one missing

(1, 2)

(2, 5)

(5, 13)

(13, 34)

(34, 89)

\dots

Commented by mr W last updated on 25/Mar/19

t h a n k y o u s i r! i n e e d t i m e t o c o m e

b e h i n d i t . i s z = 3 t h e o n l y s o l u t i o n ?

Commented by MJS last updated on 25/Mar/19

I found no other solution but I^{'} m not sure \dots

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