Discretionary decisions and sources of estimation uncertainties - Trade accounts receivable and allowance for doubtful accounts (Details) - EUR (€)	Mar. 31, 2018	Dec. 31, 2017
Trade accounts Receivable and Allowance for Doubtful Accounts
Trade accounts receivable, less allowance for doubtful accounts of 482,461 in 2016 and 427,841 in 2015	€ 3,776,566,000	€ 3,389,326,000
Allowance for doubtful accounts	€ 115,796,000	€ 474,891,000