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PEN H Problems
65
H 65
H 65
Source:
May 25, 2007
modular arithmetic
number theory
Diophantine Equations
pen
Problem Statement
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.
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