Let r= 2d-1 + 1. We investigate the diophantine inequality|∑i=1rλiΦi(xi,yi)+η||<(max?1≤i≤r{|xi|,|yi|})-σwhere Φi(x, y) ∈Z[x, y] (1≤i≤r) are nondegenerate forms of degree d= 3 or 4.
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