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Korea Contests
North Korea Team Selection Test
2013 North Korea Team Selection Test
6
6
Part of
2013 North Korea Team Selection Test
Problems
(1)
Existence of a solution of a diophantine equation
Source: North Korea Team Selection Test 2013 #6
5/17/2014
Show that
x
3
+
x
+
a
2
=
y
2
x^3 + x+ a^2 = y^2
x
3
+
x
+
a
2
=
y
2
has at least one pair of positive integer solution
(
x
,
y
)
(x,y)
(
x
,
y
)
for each positive integer
a
a
a
.
induction
number theory proposed
number theory