MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2014 India PRMO
11
11
Part of
2014 India PRMO
Problems
(1)
2014 preRMO p11, gcd, xy = x + y + (x, y)
Source:
8/9/2019
For natural numbers
x
x
x
and
y
y
y
, let
(
x
,
y
)
(x,y)
(
x
,
y
)
denote the greatest common divisor of
x
x
x
and
y
y
y
. How many pairs of natural numbers
x
x
x
and
y
y
y
with
x
≤
y
x \le y
x
≤
y
satisfy the equation
x
y
=
x
+
y
+
(
x
,
y
)
xy = x + y + (x, y)
x
y
=
x
+
y
+
(
x
,
y
)
?
number theory
greatest common divisor