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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2016 India PRMO
2
2016 preRMO p2, x^{2016}+(2016!+1!)x^{2015}+(2015!+2!)x^{2014}+...+(1!+2016!)=0
2016 preRMO p2, x^{2016}+(2016!+1!)x^{2015}+(2015!+2!)x^{2014}+...+(1!+2016!)=0
Source:
August 9, 2019
algebra
factorial
equation
diophantine
Diophantine equation
Wilson
Problem Statement
Find the number of integer solutions of the equation
x
2016
+
(
2016
!
+
1
!
)
x
2015
+
(
2015
!
+
2
!
)
x
2014
+
.
.
.
+
(
1
!
+
2016
!
)
=
0
x^{2016} + (2016! + 1!) x^{2015} + (2015! + 2!) x^{2014} + ... + (1! + 2016!) = 0
x
2016
+
(
2016
!
+
1
!)
x
2015
+
(
2015
!
+
2
!)
x
2014
+
...
+
(
1
!
+
2016
!)
=
0
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