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2013 China Western Mathematical Olympiad
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2013 China Western Mathematical Olympiad
Problems
(1)
2013 China Western Mathematical Olympiad ,Problem 1
Source: China Lanzhou 17 Aug 2013
8/17/2013
Does there exist any integer
a
,
b
,
c
a,b,c
a
,
b
,
c
such that
a
2
b
c
+
2
,
a
b
2
c
+
2
,
a
b
c
2
+
2
a^2bc+2,ab^2c+2,abc^2+2
a
2
b
c
+
2
,
a
b
2
c
+
2
,
ab
c
2
+
2
are perfect squares?
modular arithmetic
number theory proposed
number theory