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National and Regional Contests
Moldova Contests
Chisinau City MO
1973 Chisinau City MO
70
70
Part of
1973 Chisinau City MO
Problems
(1)
Chisinau MO p70 1973 p = q if naturals, p^p + q^q = p^q + q^p
Source:
3/15/2021
The natural numbers
p
,
q
p, q
p
,
q
satisfy the relation
p
p
+
q
q
=
p
q
+
q
p
p^p + q^q = p^q + q^p
p
p
+
q
q
=
p
q
+
q
p
. Prove that
p
=
q
p = q
p
=
q
.
diophantine
Diophantine equation
number theory