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Serbia Team Selection Test
2016 Serbia Additional Team Selection Test
3
3
Part of
2016 Serbia Additional Team Selection Test
Problems
(1)
Number theory, biggest odd divisor, additional TST,Serbia
Source: Serbia additional TST 2016
4/5/2016
Let
w
(
x
)
w(x)
w
(
x
)
be largest odd divisor of
x
x
x
. Let
a
,
b
a,b
a
,
b
be natural numbers such that
(
a
,
b
)
=
1
(a,b)=1
(
a
,
b
)
=
1
and \\
a
+
w
(
b
+
1
)
a+w(b+1)
a
+
w
(
b
+
1
)
and
b
+
w
(
a
+
1
)
b+w(a+1)
b
+
w
(
a
+
1
)
are powers of two. Prove that
a
+
1
a+1
a
+
1
and
b
+
1
b+1
b
+
1
are powers of two.
number theory