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Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
1
Almost binary
Almost binary
Source: St Petersburg Olympiad 2018, Grade 9, P1
July 13, 2018
number theory
Problem Statement
Prove, that for every natural
N
N
N
exists
k
k
k
, such that
N
=
a
0
2
0
+
a
1
2
1
+
.
.
.
+
a
k
2
k
N=a_02^0+a_12^1+...+a_k2^k
N
=
a
0
2
0
+
a
1
2
1
+
...
+
a
k
2
k
, where
a
0
,
a
1
,
.
.
.
a
k
a_0,a_1,...a_k
a
0
,
a
1
,
...
a
k
are
1
1
1
or
2
2
2
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