CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY - USD ($) shares in Thousands, $ in Thousands	Total	Common Stock	Additional Paid-in-Capital	Treasury Stock	Retained Earnings	Accumulated Other Comprehensive Loss
Beginning Balance (in shares) at Sep. 30, 2021		27,568
Beginning Balance at Sep. 30, 2021	$ (110,942)	$ 276	$ 1,237,348	$ (3,857,855)	$ 2,585,143	$ (75,854)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Share-based compensation	115,355		115,355
Issuance of treasury stock under employee stock plans (in shares)		264
Issuance of treasury stock under employee stock plans	(34,916)	$ 3	(53,115)	18,196
Repurchases of common stock (in shares)		(2,678)
Repurchases of common stock	(1,096,137)	$ (27)		(1,096,110)
Net income	373,541				373,541
Foreign currency translation adjustments	(48,848)					(48,848)
Ending Balance (in shares) at Sep. 30, 2022		25,154
Ending Balance at Sep. 30, 2022	(801,947)	$ 252	1,299,588	(4,935,769)	2,958,684	(124,702)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Share-based compensation	123,847		123,847
Issuance of treasury stock under employee stock plans (in shares)		231
Issuance of treasury stock under employee stock plans	(54,475)	$ 2	(72,722)	18,245
Repurchases of common stock (in shares)		(615)
Repurchases of common stock	(407,347)	$ (6)		(407,341)
Net income	429,375				429,375
Foreign currency translation adjustments	22,557					22,557
Ending Balance (in shares) at Sep. 30, 2023		24,770
Ending Balance at Sep. 30, 2023	(687,990)	$ 248	1,350,713	(5,324,865)	3,388,059	(102,145)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Share-based compensation	149,439		149,439
Issuance of treasury stock under employee stock plans (in shares)		228
Issuance of treasury stock under employee stock plans	(114,183)	$ 2	(133,580)	19,395
Repurchases of common stock (in shares)		(606)
Repurchases of common stock	(833,272)	$ (6)		(833,266)
Net income	512,811				512,811
Foreign currency translation adjustments	10,516					10,516
Ending Balance (in shares) at Sep. 30, 2024		24,392
Ending Balance at Sep. 30, 2024	$ (962,679)	$ 244	$ 1,366,572	$ (6,138,736)	$ 3,900,870	$ (91,629)