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B6
2012 PUMaC Number Theory B6
2012 PUMaC Number Theory B6
Source:
October 5, 2019
number theory
Problem Statement
Let
f
n
(
x
)
=
n
+
x
2
f_n(x) = n + x^2
f
n
(
x
)
=
n
+
x
2
. Evaluate the product
g
c
d
{
f
2001
(
2002
)
,
f
2001
(
2003
)
}
×
g
c
d
{
f
2011
(
2012
)
,
f
2011
(
2013
)
}
×
g
c
d
{
f
2021
(
2022
)
,
f
2021
(
2023
)
}
gcd\{f_{2001}(2002), f_{2001}(2003)\} \times gcd\{f_{2011}(2012), f_{2011}(2013)\} \times gcd\{f_{2021}(2022), f_{2021}(2023)\}
g
c
d
{
f
2001
(
2002
)
,
f
2001
(
2003
)}
×
g
c
d
{
f
2011
(
2012
)
,
f
2011
(
2013
)}
×
g
c
d
{
f
2021
(
2022
)
,
f
2021
(
2023
)}
, where
g
c
d
{
x
,
y
}
gcd\{x, y\}
g
c
d
{
x
,
y
}
is the greatest common divisor of
x
x
x
and
y
y
y
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