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Costa Rica Contests
Costa Rica - Final Round
2011 Costa Rica - Final Round
5
5
Part of
2011 Costa Rica - Final Round
Problems
(1)
Similar to chicken mcnugget theorem
Source: Costa Rica National Olympiad, Final Round, Problem 4
11/26/2011
Given positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
which are pairwise relatively prime, show that
2
a
b
c
−
a
b
−
b
c
−
a
c
2abc-ab-bc-ac
2
ab
c
−
ab
−
b
c
−
a
c
is the biggest number that can't be expressed in the form
x
b
c
+
y
c
a
+
z
a
b
xbc+yca+zab
x
b
c
+
yc
a
+
z
ab
with
x
,
y
,
z
x,y,z
x
,
y
,
z
being natural numbers.
number theory
relatively prime
number theory proposed