Notes to the consolidated statements of income - Treasury stock (Details) - EUR (€) € / shares in Units, € in Thousands	1 Months Ended														3 Months Ended	7 Months Ended	9 Months Ended
	Apr. 30, 2020	Mar. 31, 2020	Feb. 29, 2020	Jan. 31, 2020	Dec. 31, 2019	Nov. 30, 2019	Oct. 31, 2019	Sep. 30, 2019	Aug. 31, 2019	Jul. 31, 2019	Jun. 30, 2019	May 31, 2019	Apr. 30, 2019	Mar. 31, 2019	May 31, 2019	Dec. 31, 2019	Sep. 30, 2020	Sep. 30, 2019	Jun. 14, 2019	Dec. 31, 2018
Treasury stock
Maximum number of shares allowed to be repurchased (in shares)																			12,000,000
Maximum purchase price of shares to be repurchased																			€ 660,000
Value of treasury shares held					€ 370,502											€ 370,502	€ 736,490
Value of shares repurchased																	€ 365,988	€ 457,908
Treasury stock
Treasury stock
Average price per share, at date					€ 60.66											€ 60.66	€ 62.44			€ 51.00
Average price paid per repurchased share, during period	€ 63.07	€ 63.05	€ 249.10	€ 84.37	€ 63.85	€ 64.78	€ 57.85	€ 59.67	€ 57.53	€ 66.77	€ 67.11	€ 72.97	€ 72.83	€ 69.86	€ 71.55	€ 62.55	€ 64.35
Average price per retired share, during period											€ 71.55
Number of treasury shares held					6,107,629											6,107,629	11,795,102			999,951
Number of shares repurchased	694,813	4,842,943	25,319	124,398	564,908	852,859	692,910	627,466	835,208	1,029,655	504,672	147,558	1,993,974	1,629,240	3,770,772	5,107,678	5,687,473	6,767,773
Number of shares retired											3,770,772							3,770,772
Value of treasury shares held					€ 370,502											€ 370,502	€ 736,490			€ 50,993
Value of shares repurchased	€ 43,824	€ 305,362	€ 6,307	€ 10,495	€ 36,067	€ 55,245	€ 40,084	€ 37,445	€ 48,050	€ 68,748	€ 33,870	€ 10,766	€ 145,214	€ 113,816	€ 269,796	€ 319,509	€ 365,988	€ 457,908
Value of shares retired											€ 269,796							€ 269,796
Fees (net of taxes) paid, included in value of shares repurchased																				€ 11