MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
65
65
Part of
PEN H Problems
Problems
(1)
H 65
Source:
5/25/2007
Determine all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of integers such that
(
19
a
+
b
)
18
+
(
a
+
b
)
18
+
(
19
b
+
a
)
18
(19a+b)^{18}+(a+b)^{18}+(19b+a)^{18}
(
19
a
+
b
)
18
+
(
a
+
b
)
18
+
(
19
b
+
a
)
18
is a nonzero perfect square.
modular arithmetic
number theory
Diophantine Equations
pen