Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Aug. 31, 2025	Aug. 31, 2024
Deferred tax assets:
Accrued expenses	$ 52,850	$ 56,062
Postretirement health care and deferred compensation	56,082	58,866
Tax credit carryforwards	92,421	91,114
Loss carryforwards	114,433	88,887
Nonqualified equity	560,521	533,784
Deferred tax asset lease obligation	56,944	52,980
Deferred Tax Asset, In-Process Research and Development	115,499	69,556
Other	9,497	19,592
Deferred tax assets valuation allowance	(205,637)	(166,590)
Total deferred tax assets	852,610	804,251
Deferred Tax Assets, Net	13,950	0
Deferred tax liabilities:
Pension costs	2,083	7,003
Investments	120,667	130,171
Property, plant and equipment	601,539	618,419
Deferred tax liability right of use asset	56,250	51,872
Software costs	58,121	0
Total deferred tax liabilities	838,660	807,465
Deferred Tax Liabilities, Net	$ 0	$ 3,214