MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
Taiwan APMO Prelininary
2018 Taiwan APMO Preliminary
2
2
Part of
2018 Taiwan APMO Preliminary
Problems
(1)
Gcd, quotient
Source: 2018 Taiwan APMO preliminary
11/10/2020
Let
k
,
x
,
y
k,x,y
k
,
x
,
y
be postive integers. The quotients of
k
k
k
divided by
x
2
,
y
2
x^2, y^2
x
2
,
y
2
are
n
,
n
+
148
n,n+148
n
,
n
+
148
respectively.(
k
k
k
is divisible by
x
2
x^2
x
2
and
y
2
y^2
y
2
) (a) If
gcd
(
x
,
y
)
=
1
\gcd(x,y)=1
g
cd
(
x
,
y
)
=
1
, then find
k
k
k
. (b) If
gcd
(
x
,
y
)
=
4
\gcd(x,y)=4
g
cd
(
x
,
y
)
=
4
, then find
k
k
k
.
number theory