Soybean (Glycine max L.) is one of the most important crops grown globally. Biochar has been proposed as an alternative to aid sustainable soybean production. However, comprehensive studies that include both the economic aspects of soybean production and biochar are scarce. Poland, with an economy largely based on agriculture, is an interesting case to investigate the cost-effectiveness of using biochar in soybean production. We show that the use of biochar at rates of 40, 60 and 80 t/ha is unprofitable compared with a traditional soil amendment, such as NPK fertilization. The breakeven price for biochar to be economically viable should be USD 39.22, USD 38.29 and USD 23.53 for 40, 60 and 80 Mg/ha biochar, respectively, while the cost of biochar used for this experiment was USD 85.33. The payback period for doses of 40 and 60 Mg/ha was estimated to be three years. With a carbon sequestration subsidy of USD 30 per ton of CO2, the use of biochar may be profitable in the first year of soybean production. This is the first comprehensive economic analysis of the use of biochar in soybean production in Poland and one of the few published worldwide.

We conjecture that if a system S ⊆ {x i + x j = x k , x i • x j = x k : i, j, k ∈ {1,. .. , n}} has only finitely many solutions in integers x 1 ,. .. , x n , then each such solution (x 1 ,. .. , x n) satisfies max |x 1 |,. .. , |x n | ≤ 2 2 n−1. The conjecture implies that there is an algorithm which to each Diophantine equation assigns an integer which is greater than the heights of integer (non-negative integer, rational) solutions, if these solutions form a finite set. We describe an algorithm whose execution never terminates. If the conjecture is true, then the algorithm sequentially displays all integers n ≥ 2. If the conjecture is false, then the algorithm has a finite output which ends with an integer tuple (a 1 ,. .. , a n), where n ≥ 4, 2 2 n−1 < max |a 1 |,. .. , |a n | ≤ 2 2 n , and the system {x i + x j = x k : (i, j, k ∈ {1,. .. , n}) ∧ (a i + a j = a k)} ∪ {x i • x j = x k : (i, j, k ∈ {1,. .. , n}) ∧ (a i • a j = a k)} is a counterexample to the conjecture. The algorithm is implemented in MuPAD and Pascal.

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Abstract-The height of a rational number

A modern model of agriculture is based on three orders - organic, social and economic. An attempt was made in this paper to apply cluster analysis for assessment of economic and organic sustainability of organic farms. Factors that statistically influenced a decision on which farms should be recognised as sustainable were indicated. Analyses allow the following conclusion: 1) in organic farming, animal production including cattle breeding and rearing must be based on a high acreage of permanent grasslands; 2) neither the performed production processes nor the level of their automation rate or the level of organic balance do not decide on the production effectiveness, but factors of the surrounding including social factors.