MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2017 Swedish Mathematical Competition
2
2
Part of
2017 Swedish Mathematical Competition
Problems
(1)
(p+m)/(p+n)= m/n + 1/p^2
Source: 2017 Swedish Mathematical Competition p2
5/1/2021
Let
p
p
p
be a prime number. Find all pairs of coprime positive integers
(
m
,
n
)
(m,n)
(
m
,
n
)
such that
p
+
m
p
+
n
=
m
n
+
1
p
2
.
\frac{p+m}{p+n}=\frac{m}{n}+\frac{1}{p^2}.
p
+
n
p
+
m
=
n
m
+
p
2
1
.
number theory
Diophantine equation
diophantine