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India Contests
India EGMO TST
India EGMO 2023 TST
2
2
Part of
India EGMO 2023 TST
Problems
(1)
Alice takes beet, no, cube roots!
Source: India EGMO TST 2023/2
12/10/2022
Alice has an integer
N
>
1
N > 1
N
>
1
on the blackboard. Each minute, she deletes the current number
x
x
x
on the blackboard and writes
2
x
+
1
2x+1
2
x
+
1
if
x
x
x
is not the cube of an integer, or the cube root of
x
x
x
otherwise. Prove that at some point of time, she writes a number larger than
1
0
100
10^{100}
1
0
100
.Proposed by Anant Mudgal and Rohan Goyal
number theory