MathDB
Problems
Contests
International Contests
Lusophon Mathematical Olympiad
2019 Lusophon Mathematical Olympiad
5
5
Part of
2019 Lusophon Mathematical Olympiad
Problems
(1)
2018 = A^5 + B^5 + C^5 + D^5 + E^5, 2018 = A^5 + B^5 + C^5 + D^5
Source: Lusophon 2019 CPLP P5
12/31/2019
a) Show that there are five integers
A
,
B
,
C
,
D
A, B, C, D
A
,
B
,
C
,
D
, and
E
E
E
such that
2018
=
A
5
+
B
5
+
C
5
+
D
5
+
E
5
2018 = A^5 + B^5 + C^5 + D^5 + E^5
2018
=
A
5
+
B
5
+
C
5
+
D
5
+
E
5
b) Show that there are no four integers
A
,
B
,
C
A, B, C
A
,
B
,
C
and
D
D
D
such that
2018
=
A
5
+
B
5
+
C
5
+
D
5
2018 = A^5 + B^5 + C^5 + D^5
2018
=
A
5
+
B
5
+
C
5
+
D
5
number theory
Sum of powers