MathDB
Problems
Contests
International Contests
Rioplatense Mathematical Olympiad, Level 3
2017 Rioplatense Mathematical Olympiad, Level 3
1
1
Part of
2017 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
(x+a)(x+b)=x+a+b diophantine
Source: Rioplatense 2017 L3 P1
10/19/2022
Let
a
a
a
be a fixed positive integer. Find the largest integer
b
b
b
such that
(
x
+
a
)
(
x
+
b
)
=
x
+
a
+
b
(x+a)(x+b)=x+a+b
(
x
+
a
)
(
x
+
b
)
=
x
+
a
+
b
, for some integer
x
x
x
.
number theory
diophantine
Diophantine equation