Consolidated Statements of Changes in Stockholders' Equity - USD ($) $ in Thousands	Total	Common Stock	Additional Paid-in Capital	Treasury Stock	Retained Earnings	Accumulated Other Comprehensive Loss
Balance, beginning of period (in shares) at Aug. 31, 2022		41,653,218
Beginning balance at Aug. 31, 2022	$ 1,331,408	$ 417	$ 1,190,350	$ (930,715)	$ 1,179,739	$ (108,383)
Beginning balance, treasury stock (in shares) at Aug. 31, 2022				3,608,462
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	468,173				468,173
Other comprehensive income (loss)	21,242					21,242
Common stock issued for employee stock plans (in shares)		360,375		410
Common stock issued for employee stock plans	71,840	$ 3	72,003	$ (166)
Vesting of restricted stock (in shares)		83,035		32,034
Vesting of restricted stock	(13,544)	$ 1	(1)	$ (13,544)
Excise tax on share repurchases	$ (932)			$ (932)
Repurchase of common stock (in shares)	430,350			430,350
Repurchases of common stock	$ (176,720)			$ (176,720)
Stock-based compensation expense	62,038		62,038
Dividends declared	(142,816)				(142,816)
Other	(759)		(759)
Balance, end of period (in shares) at Aug. 31, 2023		42,096,628
Ending balance at Aug. 31, 2023	1,619,930	$ 421	1,323,631	$ (1,122,077)	1,505,096	(87,141)
Ending balance, treasury stock (in shares) at Aug. 31, 2023				4,071,256
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	537,126				537,126
Other comprehensive income (loss)	7,528					7,528
Common stock issued for employee stock plans (in shares)		407,542		831
Common stock issued for employee stock plans	91,336	$ 4	91,708	$ (376)
Vesting of restricted stock (in shares)		94,745		36,758
Vesting of restricted stock	(16,283)	$ 1	(1)	$ (16,283)
Excise tax on share repurchases	$ (1,725)			$ (1,725)
Repurchase of common stock (in shares)	537,800			537,800
Repurchases of common stock	$ (235,235)			$ (235,235)
Stock-based compensation expense	63,501		63,501
Dividends declared	$ (153,718)				(153,718)
Balance, end of period (in shares) at Aug. 31, 2024	37,952,270	42,598,915
Ending balance at Aug. 31, 2024	$ 1,912,460	$ 426	1,478,839	$ (1,375,696)	1,888,504	(79,613)
Ending balance, treasury stock (in shares) at Aug. 31, 2024	4,646,645			4,646,645
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 597,040				597,040
Other comprehensive income (loss)	15,865					15,865
Common stock issued for employee stock plans (in shares)		325,030		370
Common stock issued for employee stock plans	81,519	$ 3	81,686	$ (170)
Vesting of restricted stock (in shares)		89,321		35,421
Vesting of restricted stock	(16,072)	$ 1	(1)	$ (16,072)
Excise tax on share repurchases	$ (3,034)			$ (3,034)
Repurchase of common stock (in shares)	684,960			684,960
Repurchases of common stock	$ (300,457)			$ (300,457)
Stock-based compensation expense	61,229		61,229
Dividends declared	$ (162,137)				(162,137)
Balance, end of period (in shares) at Aug. 31, 2025	37,645,870	43,013,266
Ending balance at Aug. 31, 2025	$ 2,186,413	$ 430	$ 1,621,753	$ (1,695,429)	$ 2,323,407	$ (63,748)
Ending balance, treasury stock (in shares) at Aug. 31, 2025	5,367,396			5,367,396