MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2017
P1
Perfect Cubes
Perfect Cubes
Source: 2013 USAJMO Problem 1
April 30, 2013
modular arithmetic
Euler
LaTeX
number theory
relatively prime
Problem Statement
Are there integers
a
a
a
and
b
b
b
such that
a
5
b
+
3
a^5b+3
a
5
b
+
3
and
a
b
5
+
3
ab^5+3
a
b
5
+
3
are both perfect cubes of integers?
Back to Problems
View on AoPS