MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia TST
2010 Indonesia TST
4
Indonesian TST 2010 Problem 3 Test 3 Stage 3
Indonesian TST 2010 Problem 3 Test 3 Stage 3
Source:
December 13, 2010
number theory unsolved
number theory
Problem Statement
How many natural numbers
(
a
,
b
,
n
)
(a,b,n)
(
a
,
b
,
n
)
with
g
c
d
(
a
,
b
)
=
1
gcd(a,b)=1
g
c
d
(
a
,
b
)
=
1
and
n
>
1
n>1
n
>
1
such that the equation
x
a
n
+
y
b
n
=
2
2010
x^{an} +y^{bn} = 2^{2010}
x
an
+
y
bn
=
2
2010
has natural numbers solution
(
x
,
y
)
(x,y)
(
x
,
y
)
Back to Problems
View on AoPS