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CHMMC problems
2021 CHMMC Winter (2021-22)
4
CHMMC 2021-22 Proof 4
CHMMC 2021-22 Proof 4
Source:
September 1, 2022
number theory
Problem Statement
Show that for any three positive integers
a
,
m
,
n
a,m,n
a
,
m
,
n
such that
m
m
m
divides
n
n
n
, there exists an integer
k
k
k
such that
g
c
d
(
a
,
m
)
=
g
c
d
(
a
+
k
m
,
n
)
gcd(a,m) = gcd(a+km,n)
g
c
d
(
a
,
m
)
=
g
c
d
(
a
+
km
,
n
)
.
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