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National and Regional Contests
China Contests
(China) National High School Mathematics League
2015 China Second Round Olympiad
3
Infinitely many triplets
Infinitely many triplets
Source: China Second Round 2015 (B) Q3
May 5, 2016
number theory
Problem Statement
Prove that there exist infinitely many positive integer triples
(
a
,
b
,
c
)
(
a
,
b
,
c
>
2015
)
(a,b,c)(a,b,c>2015)
(
a
,
b
,
c
)
(
a
,
b
,
c
>
2015
)
such that
a
∣
b
c
−
1
,
b
∣
a
c
+
1
,
c
∣
a
b
+
1.
a|bc-1, b|ac+1, c|ab+1.
a
∣
b
c
−
1
,
b
∣
a
c
+
1
,
c
∣
ab
+
1.
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