MathDB

Suppose that

a_1, a_2, a_3, \ldots

is an infinite geometric sequence such that for all

i \ge 1

a_i

is a positive integer. Suppose furthermore that

a_{20} + a_{21} = 20^{21}

. If the minimum possible value of

a_1

can be expressed as

2^a 5^b

for positive integers

a

and

b

, find

a + b

.
Proposed by Andrew Wu

Problem Statement