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Gulf Math Olympiad
2017 Gulf Math Olympiad
4
4
Part of
2017 Gulf Math Olympiad
Problems
(1)
max power of 2 that divides \lceil(1+\sqrt{3})^{2n}\rceil for pos. integer n
Source: Gulf Mathematical Olympiad GMO 2017 p4
8/23/2019
1 - Prove that
55
<
(
1
+
3
)
4
<
56
55 < (1+\sqrt{3})^4 < 56
55
<
(
1
+
3
)
4
<
56
.2 - Find the largest power of
2
2
2
that divides
⌈
(
1
+
3
)
2
n
⌉
\lceil(1+\sqrt{3})^{2n}\rceil
⌈(
1
+
3
)
2
n
⌉
for the positive integer
n
n
n
ceiling function
power of 2
divides
maximum
number theory