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Mexico Contests
Mexico National Olympiad
1988 Mexico National Olympiad
2
2
Part of
1988 Mexico National Olympiad
Problems
(1)
11a+2b is a multiple of 19 iff so is 18a+5b .
Source: Mexican Mathematical Olympiad 1988 OMM P2
7/27/2018
If
a
a
a
and
b
b
b
are positive integers, prove that
11
a
+
2
b
11a+2b
11
a
+
2
b
is a multiple of
19
19
19
if and only if so is
18
a
+
5
b
18a+5b
18
a
+
5
b
.
number theory
divisor