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2007 Spain Mathematical Olympiad
Problem 2
Problem 2
Part of
2007 Spain Mathematical Olympiad
Problems
(1)
2007 Spain Mathematical Olympiad, Problem 2
Source: Spain Mathematical Olympiad 2007
6/8/2017
Determine all the possible non-negative integer values that are able to satisfy the expression:
(
m
2
+
m
n
+
n
2
)
(
m
n
−
1
)
\frac{(m^2+mn+n^2)}{(mn-1)}
(
mn
−
1
)
(
m
2
+
mn
+
n
2
)
if
m
m
m
and
n
n
n
are non-negative integers such that
m
n
≠
1
mn \neq 1
mn
=
1
.
algebra
number theory