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India Pre-Regional Mathematical Olympiad
2012 India PRMO
9
2012 preRMO p9 , product X_1X_2... X_{124}
2012 preRMO p9 , product X_1X_2... X_{124}
Source:
June 16, 2019
algebra
Problem Statement
Suppose that
4
x
1
=
5
,
5
x
2
=
6
,
6
x
3
=
7
,
.
.
.
,
12
6
x
123
=
127
,
12
7
x
124
=
128
4^{x_1}= 5, 5^{x_2}= 6,6^{x_3} = 7,..., 126^{x_{123}} = 127,127^{x_{124}} = 128
4
x
1
=
5
,
5
x
2
=
6
,
6
x
3
=
7
,
...
,
12
6
x
123
=
127
,
12
7
x
124
=
128
. What is the value of the product
X
1
X
2
.
.
.
X
124
X_1X_2... X_{124}
X
1
X
2
...
X
124
?
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