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Korea Summer Program Practice Test
2016 Korea Summer Program Practice Test
1
1
Part of
2016 Korea Summer Program Practice Test
Problems
(1)
Iterative system of equations
Source: Korean Summer Program Practice Test 2016 1
8/17/2016
Find all real numbers
x
1
,
…
,
x
2016
x_1, \dots, x_{2016}
x
1
,
…
,
x
2016
that satisfy the following equation for each
1
≤
i
≤
2016
1 \le i \le 2016
1
≤
i
≤
2016
. (Here
x
2017
=
x
1
x_{2017} = x_1
x
2017
=
x
1
.)
x
i
2
+
x
i
−
1
=
x
i
+
1
x_i^2 + x_i - 1 = x_{i+1}
x
i
2
+
x
i
−
1
=
x
i
+
1
algebra
system of equations