MathDB
Problems
Contests
International Contests
Austrian-Polish
1990 Austrian-Polish Competition
2
2
Part of
1990 Austrian-Polish Competition
Problems
(1)
a^A = b^B = c^C = 1990^{1990}abc where A = b^c, B = c^a, C = a^b
Source: Austrian - Polish 1990 APMC
5/7/2020
Find all solutions in positive integers to
a
A
=
b
B
=
c
C
=
199
0
1990
a
b
c
a^A = b^B = c^C = 1990^{1990}abc
a
A
=
b
B
=
c
C
=
199
0
1990
ab
c
, where
A
=
b
c
,
B
=
c
a
,
C
=
a
b
A = b^c, B = c^a, C = a^b
A
=
b
c
,
B
=
c
a
,
C
=
a
b
.
diophantine
Diophantine equation
number theory