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Diophantine equation with no solutions

Source: Miklos Schweitzer 2013

January 26, 2014
algebrapolynomialVietanumber theory unsolvednumber theory

Problem Statement

Prove there exists a constant k0k_0 such that for any k≥k0k\ge k_0, the equation a2n+b4n+2013=kanb2na^{2n}+b^{4n}+2013=ka^nb^{2n} has no positive integer solutions a,b,na,b,n.
Proposed by István Pink.
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