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International Contests
Tournament Of Towns
1995 Tournament Of Towns
(478) 2
(478) 2
Part of
1995 Tournament Of Towns
Problems
(1)
TOT 478 1995 Autumn S A2 n irrationals if their product -x_= odd integer
Source:
7/9/2024
Let
p
p
p
be the product of
n
n
n
real numbers
x
1
x_1
x
1
,
x
2
x_2
x
2
,
.
.
.
...
...
,
x
n
x_n
x
n
. Prove that if
p
−
x
k
p - x_k
p
−
x
k
is an odd integer for
k
=
1
,
2
,
.
.
.
,
n
k = 1, 2,..., n
k
=
1
,
2
,
...
,
n
, then each of the numbers
x
1
x_1
x
1
,
x
2
x_2
x
2
,
.
.
.
...
...
,
x
n
x_n
x
n
is irrational. (G Galperin)
irrational number
number theory
algebra