Income Taxes, Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 03, 2025	Sep. 27, 2024	Sep. 29, 2023
Income Tax Disclosure [Abstract]
Tax expense at United States statutory rate	$ 110.6	$ 133.6	$ 226.5
Foreign tax rate difference	(22.0)	(84.7)	(90.7)
Effect of stock compensation	10.2	11.3	16.0
Research and development credits	(44.5)	(28.7)	(29.7)
Change in tax reserve	(1.4)	11.1	8.1
Global Intangible Low-Taxed Income	4.0	18.1	16.3
Foreign Derived Intangible Income	(44.7)	(49.3)	(65.9)
Section 162(m) limitation	15.8	10.6	10.9
Remeasurement of concessionary tax rate	19.0	0.0	0.0
Other, net	2.6	18.4	4.5
Provision for income taxes	$ 49.6	$ 40.4	$ 96.0