MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
1953 Polish MO Finals
4
4
Part of
1953 Polish MO Finals
Problems
(1)
(\sqrt{2}- 1)^n = \sqrt{m} - \sqrt{m-1}
Source: Polish MO Finals 1953 p4
8/29/2024
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.
algebra
number theory