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Number theory shortlist jbmo 2018
Number theory shortlist jbmo 2018
Source: JBMO 2018 SHL
July 11, 2019
number theory proposed
number theory
Problem Statement
Find all positive integers
a
b
c
d
=
a
a
+
b
+
c
+
d
−
a
−
a
+
b
−
c
+
d
+
a
abcd=a^{a+b+c+d} - a^{-a+b-c+d} + a
ab
c
d
=
a
a
+
b
+
c
+
d
−
a
−
a
+
b
−
c
+
d
+
a
, where
a
b
c
d
abcd
ab
c
d
is a four-digit number
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