MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2008 Saint Petersburg Mathematical Olympiad
5
St Petersburgh 2008 #5
St Petersburgh 2008 #5
Source:
July 23, 2011
modular arithmetic
quadratics
number theory proposed
number theory
Problem Statement
Given are distinct natural numbers
a
a
a
,
b
b
b
, and
c
c
c
. Prove that
gcd
(
a
b
+
1
,
a
c
+
1
,
b
c
+
1
)
≤
a
+
b
+
c
3
\gcd(ab+1, ac+1, bc+1)\le \frac{a+b+c}{3}
g
cd
(
ab
+
1
,
a
c
+
1
,
b
c
+
1
)
≤
3
a
+
b
+
c
Back to Problems
View on AoPS