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Regional Mathematical Olympiad
2017 India Regional Mathematical Olympiad
2
RMO 2017 P2
RMO 2017 P2
Source: RMO 2017 P2
October 8, 2017
modular arithmetic
number theory
Problem Statement
Show that the equation
a
3
+
(
a
+
1
)
3
+
…
+
(
a
+
6
)
3
=
b
4
+
(
b
+
1
)
4
a^3+(a+1)^3+\ldots+(a+6)^3=b^4+(b+1)^4
a
3
+
(
a
+
1
)
3
+
…
+
(
a
+
6
)
3
=
b
4
+
(
b
+
1
)
4
has no solutions in integers
a
,
b
a,b
a
,
b
.
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