MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAMO
2015 USAMO
5
On a^4+b^4=c^4+d^4=e^5
On a^4+b^4=c^4+d^4=e^5
Source: USAMO 2015, Problem 5
April 29, 2015
Diophantine equation
USAMO
number theory
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
,
e
e
e
be distinct positive integers such that
a
4
+
b
4
=
c
4
+
d
4
=
e
5
a^4+b^4=c^4+d^4=e^5
a
4
+
b
4
=
c
4
+
d
4
=
e
5
. Show that
a
c
+
b
d
ac+bd
a
c
+
b
d
is a composite number.
Back to Problems
View on AoPS