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Girls in Math at Yale
2021 Girls in Math at Yale
10
10
Part of
2021 Girls in Math at Yale
Problems
(1)
Girls in Math at Yale 2021 Problem 10: 20^21
Source:
2/27/2021
Suppose that
a
1
,
a
2
,
a
3
,
…
a_1, a_2, a_3, \ldots
a
1
,
a
2
,
a
3
,
…
is an infinite geometric sequence such that for all
i
≥
1
i \ge 1
i
≥
1
,
a
i
a_i
a
i
is a positive integer. Suppose furthermore that
a
20
+
a
21
=
2
0
21
a_{20} + a_{21} = 20^{21}
a
20
+
a
21
=
2
0
21
. If the minimum possible value of
a
1
a_1
a
1
can be expressed as
2
a
5
b
2^a 5^b
2
a
5
b
for positive integers
a
a
a
and
b
b
b
, find
a
+
b
a + b
a
+
b
.Proposed by Andrew Wu
Yale
college