MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2003 Bosnia and Herzegovina Junior BMO TST
3
3
Part of
2003 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
a^3 + b^3 + c^3 is divisible by 6
Source: 2003 Bosnia & Herzegovina JBMO TST p3
5/27/2020
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be integers such that the number
a
2
+
b
2
+
c
2
a^2 +b^2 +c^2
a
2
+
b
2
+
c
2
is divisible by
6
6
6
and the number
a
b
+
b
c
+
c
a
ab + bc + ca
ab
+
b
c
+
c
a
is divisible by
3
3
3
. Prove that the number
a
3
+
b
3
+
c
3
a^3 + b^3 + c^3
a
3
+
b
3
+
c
3
is divisible by
6
6
6
.
divides
divisible
number theory