Shareholders' Equity (Narrative) (Details) $ in Thousands		12 Months Ended
	Feb. 14, 2023 shares	Aug. 31, 2024 USD ($) shares	Aug. 31, 2023 USD ($) shares	Aug. 31, 2022 USD ($) shares
Class of Stock [Line Items]
Excise tax, percent		1
Shares of preferred stock authorized for issuance		14,000,000.0
Preferred stock issued			0	0
Preferred stock outstanding		0	0
Purchase of treasury shares | $		$ 30,749	$ 35,555	$ 23,850
Open market purchases, Shares	50,000,000.0	524,548	867,873	499,411
Open market purchases, Cost | $		$ 20,416	$ 34,720	$ 20,315
Open Market Purchases [Member]
Class of Stock [Line Items]
Purchase of treasury shares | $		$ 20,400
Open market purchases, Shares		524,548
Upon Approval of Purchase Plan [Member]
Class of Stock [Line Items]
Purchase of treasury shares | $		$ 4,900
Open market purchases, Shares		127,252