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India IMO Training Camp
2019 India IMO Training Camp
P2
Numbers not power of 5
Numbers not power of 5
Source: Indian TST D1 P2
July 17, 2019
number theory
Problem Statement
Show that there do not exist natural numbers
a
1
,
a
2
,
…
,
a
2018
a_1, a_2, \dots, a_{2018}
a
1
,
a
2
,
…
,
a
2018
such that the numbers
(
a
1
)
2018
+
a
2
,
(
a
2
)
2018
+
a
3
,
…
,
(
a
2018
)
2018
+
a
1
(a_1)^{2018}+a_2, (a_2)^{2018}+a_3, \dots, (a_{2018})^{2018}+a_1
(
a
1
)
2018
+
a
2
,
(
a
2
)
2018
+
a
3
,
…
,
(
a
2018
)
2018
+
a
1
are all powers of
5
5
5
Proposed by Tejaswi Navilarekallu
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