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Problems
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National and Regional Contests
Chile Contests
Chile National Olympiad
1991 Chile National Olympiad
4
4
Part of
1991 Chile National Olympiad
Problems
(1)
2x + 3y, 9x + 5y both divisible by 17 (Chile NMO 1991 P4)
Source:
11/20/2021
Show that the expressions
2
x
+
3
y
2x + 3y
2
x
+
3
y
,
9
x
+
5
y
9x + 5y
9
x
+
5
y
are both divisible by
17
17
17
, for the same values of
x
x
x
and
y
y
y
.
number theory
divides
divisible