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2010 JBMO Shortlist
2
JBMO 2010 Shortlist A2
JBMO 2010 Shortlist A2
Source: JBMO 2010 Shortlist
June 28, 2017
algebra
number theory
equation
JBMO Shortlist
Problem Statement
Determine all four digit numbers
a
ˉ
b
ˉ
c
ˉ
d
ˉ
\bar{a}\bar{b}\bar{c}\bar{d}
a
ˉ
b
ˉ
c
ˉ
d
ˉ
such that
a
(
a
+
b
+
c
+
d
)
(
a
2
+
b
2
+
c
2
+
d
2
)
(
a
6
+
2
b
6
+
3
c
6
+
4
d
6
)
=
a
ˉ
b
ˉ
c
ˉ
d
ˉ
a(a+b+c+d)(a^{2}+b^{2}+c^{2}+d^{2})(a^{6}+2b^{6}+3c^{6}+4d^{6})=\bar{a}\bar{b}\bar{c}\bar{d}
a
(
a
+
b
+
c
+
d
)
(
a
2
+
b
2
+
c
2
+
d
2
)
(
a
6
+
2
b
6
+
3
c
6
+
4
d
6
)
=
a
ˉ
b
ˉ
c
ˉ
d
ˉ
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