Stockholders' Equity - Schedule of Common Stock Outstanding (Details) - shares	3 Months Ended		6 Months Ended			12 Months Ended
	Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Aug. 31, 2025	Feb. 28, 2025	Aug. 31, 2025
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)			107,480,895
Treasury shares purchased (in shares)	(500,000)	(700,000)	(1,700,000)		(2,500,000)
Common stock outstanding, ending balance (in shares)	105,818,234		105,818,234	107,480,895		107,480,895
Common stock:
Common stock outstanding:
Common stock outstanding, beginning balances (in shares)	106,822,960	111,693,059	107,480,895	109,539,804	113,744,167	113,744,167
Shares issued under employee stock purchase plan (in shares)	210,729	355,851	210,750		355,851
Vesting of restricted stock (in shares)	13,111	6,419	1,101,759		1,089,031
Purchases of treasury stock under employee stock plans (in shares)	(873)	(991)	(315,109)		(323,991)
Treasury shares purchased (in shares)	(1,227,693)	(2,514,534)	(2,660,061)		(5,325,254)
Common stock outstanding, ending balance (in shares)	105,818,234	109,539,804	105,818,234	107,480,895	109,539,804	107,480,895