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Miklós Schweitzer
2013 Miklós Schweitzer
2
2
Part of
2013 Miklós Schweitzer
Problems
(1)
Diophantine equation with no solutions
Source: Miklos Schweitzer 2013
1/26/2014
Prove there exists a constant
k
0
k_0
k
0
such that for any
k
≥
k
0
k\ge k_0
k
≥
k
0
, the equation
a
2
n
+
b
4
n
+
2013
=
k
a
n
b
2
n
a^{2n}+b^{4n}+2013=ka^nb^{2n}
a
2
n
+
b
4
n
+
2013
=
k
a
n
b
2
n
has no positive integer solutions
a
,
b
,
n
a,b,n
a
,
b
,
n
.Proposed by István Pink.
algebra
polynomial
Vieta
number theory unsolved
number theory