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Regional Mathematical Olympiad
2005 India Regional Mathematical Olympiad
2
Divides
Divides
Source: Indian RMO 2005 Problem 2
February 28, 2006
Problem Statement
If
x
,
y
x,y
x
,
y
are integers and
17
17
17
divides both
x
2
−
2
x
y
+
y
2
−
5
x
+
7
y
x^2 -2xy + y^2 -5x + 7y
x
2
−
2
x
y
+
y
2
−
5
x
+
7
y
and
x
2
−
3
x
y
+
2
y
2
+
x
−
y
x^2 - 3xy + 2y^2 + x - y
x
2
−
3
x
y
+
2
y
2
+
x
−
y
, then prove that
17
17
17
divides
x
y
−
12
x
+
15
y
xy - 12x + 15y
x
y
−
12
x
+
15
y
.
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