MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2008 Saint Petersburg Mathematical Olympiad
6
Maximum GCD
Maximum GCD
Source: St Petersburg Olympiad 2008, Grade 11, P6
August 30, 2017
number theory
greatest common divisor
Problem Statement
a
+
b
+
c
≤
3000000
a+b+c \leq 3000000
a
+
b
+
c
≤
3000000
and
a
≠
b
≠
c
≠
a
a\neq b \neq c \neq a
a
=
b
=
c
=
a
and
a
,
b
,
c
a,b,c
a
,
b
,
c
are naturals. Find maximum
G
C
D
(
a
b
+
1
,
a
c
+
1
,
b
c
+
1
)
GCD(ab+1,ac+1,bc+1)
GC
D
(
ab
+
1
,
a
c
+
1
,
b
c
+
1
)
Back to Problems
View on AoPS