MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2003 India IMO Training Camp
2
2
Part of
2003 India IMO Training Camp
Problems
(1)
find all triples (a,b,c)
Source: India tst 2003, p2
3/14/2012
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of positive integers such that (i)
a
≤
b
≤
c
a \leq b \leq c
a
≤
b
≤
c
; (ii)
gcd
(
a
,
b
,
c
)
=
1
\text{gcd}(a,b,c)=1
gcd
(
a
,
b
,
c
)
=
1
; and (iii)
a
3
+
b
3
+
c
3
a^3+b^3+c^3
a
3
+
b
3
+
c
3
is divisible by each of the numbers
a
2
b
,
b
2
c
,
c
2
a
a^2b, b^2c, c^2a
a
2
b
,
b
2
c
,
c
2
a
.
number theory
greatest common divisor
number theory proposed