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1953 Polish MO Finals
4
(\sqrt{2}- 1)^n = \sqrt{m} - \sqrt{m-1}
(\sqrt{2}- 1)^n = \sqrt{m} - \sqrt{m-1}
Source: Polish MO Finals 1953 p4
August 29, 2024
algebra
number theory
Problem Statement
Prove that if
n
n
n
is a natural number, then equality holds
(
2
−
1
)
n
=
m
−
m
−
1
(\sqrt{2}- 1)^n = \sqrt{m} - \sqrt{m-1}
(
2
−
1
)
n
=
m
−
m
−
1
where
m
m
m
is a natural number.
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