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Contests
National and Regional Contests
Cuba Contests
Cuba MO
2015 Cuba MO
7
7
Part of
2015 Cuba MO
Problems
(1)
p(x -2) = x(y -1) , diophantine
Source: 2015 Cuba 2.7
9/20/2024
If
p
p
p
is a prime number and
x
,
y
x, y
x
,
y
are positive integers, find in terms of
p
p
p
, all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
that satisfy the equation:
p
(
x
−
2
)
=
x
(
y
−
1
)
.
p(x -2) = x(y -1).
p
(
x
−
2
)
=
x
(
y
−
1
)
.
If
x
+
y
=
21
x+y = 21
x
+
y
=
21
, find all triples
(
x
,
y
,
p
)
(x, y, p)
(
x
,
y
,
p
)
that satisfy this equation.
number theory
diophantine
Diophantine equation