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Polish MO Finals
1958 Polish MO Finals
4
4
Part of
1958 Polish MO Finals
Problems
(1)
(1 + x)(1 + x^2) (1 + x^4) ...(1 + x^{2^k}) = 1 + x + x^2 + x^3+ .. x^m
Source: Polish MO Finals 1958 p4
8/29/2024
Prove that if
k
k
k
is a natural number, then
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
…
(
1
+
x
2
k
)
=
1
+
x
+
x
2
+
x
3
+
…
+
x
m
(1 + x)(1 + x^2) (1 + x^4) \ldots (1 + x^{2^k}) =1 + x + x^2 + x^3+ \ldots + x^m
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
…
(
1
+
x
2
k
)
=
1
+
x
+
x
2
+
x
3
+
…
+
x
m
where
m
m
m
is a natural number dependent on
k
k
k
; determine
m
m
m
.
algebra