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2022 HMIC
1
Rational Infinite Product
Rational Infinite Product
Source: HMIC 2022/1
April 8, 2022
number theory
Problem Statement
Is
∏
k
=
0
∞
(
1
−
1
202
2
k
!
)
\prod_{k=0}^\infty \left(1-\frac{1}{2022^{k!}}\right)
k
=
0
∏
∞
(
1
−
202
2
k
!
1
)
rational?
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