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Show that k exists
Show that k exists
Source: SAMO 2022, Senior R3, P3
July 28, 2022
number theory
GCD
number theory unsolved
Problem Statement
Let a, b, and c be nonzero integers. Show that there exists an integer k such that
g
c
d
(
a
+
k
b
,
c
)
=
g
c
d
(
a
,
b
,
c
)
gcd\left(a+kb, c\right) = gcd\left(a, b, c\right)
g
c
d
(
a
+
kb
,
c
)
=
g
c
d
(
a
,
b
,
c
)
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