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China National Olympiad
1991 China National Olympiad
4
4
Part of
1991 China National Olympiad
Problems
(1)
China Mathematical Olympiad 1991 problem4
Source: China Mathematical Olympiad 1991 problem4
10/8/2013
Find all positive integer solutions
(
x
,
y
,
z
,
n
)
(x,y,z,n)
(
x
,
y
,
z
,
n
)
of equation
x
2
n
+
1
−
y
2
n
+
1
=
x
y
z
+
2
2
n
+
1
x^{2n+1}-y^{2n+1}=xyz+2^{2n+1}
x
2
n
+
1
−
y
2
n
+
1
=
x
yz
+
2
2
n
+
1
, where
n
≥
2
n\ge 2
n
≥
2
and
z
≤
5
×
2
2
n
z \le 5\times 2^{2n}
z
≤
5
×
2
2
n
.
number theory unsolved
number theory