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2019 MOAA
8
2019 MOAA Team P8
2019 MOAA Team P8
Source:
January 23, 2022
algebra
team
2019
Problem Statement
Suppose that
(
2
)
5
+
1
2
+
1
×
2
5
+
1
2
+
1
×
4
5
+
1
4
+
1
×
1
6
5
+
1
16
+
1
=
m
7
+
3
2
\frac{(\sqrt2)^5 + 1}{\sqrt2 + 1} \times \frac{2^5 + 1}{2 + 1} \times \frac{4^5 + 1}{4 + 1} \times \frac{16^5 + 1}{16 + 1} =\frac{m}{7 + 3\sqrt2}
2
+
1
(
2
)
5
+
1
×
2
+
1
2
5
+
1
×
4
+
1
4
5
+
1
×
16
+
1
1
6
5
+
1
=
7
+
3
2
m
for some integer
m
m
m
. How many
0
0
0
’s are in the binary representation of
m
m
m
? (For example, the number
20
=
1010
0
2
20 = 10100_2
20
=
1010
0
2
has three
0
0
0
’s in its binary representation.)
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