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Saint Petersburg Mathematical Olympiad
2009 Saint Petersburg Mathematical Olympiad
1
GCD of degrees
GCD of degrees
Source: St Petersburg Olympiad 2009, Grade 10, P1
August 30, 2017
number theory
greatest common divisor
Problem Statement
x
,
y
x,y
x
,
y
are naturals.
G
C
M
(
x
7
,
y
4
)
ā
G
C
M
(
x
8
,
y
5
)
=
x
y
GCM(x^7,y^4)*GCM(x^8,y^5)=xy
GCM
(
x
7
,
y
4
)
ā
GCM
(
x
8
,
y
5
)
=
x
y
Prove that
x
y
xy
x
y
is cube
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