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Stockholders' Equity (Weighted Average Grant Date Fair Value of Options Granted) (Details) - $ / shares
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Stock Options [Member]      
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]      
Weighted-average grant date fair value of options $ 58.34 $ 34.19 $ 41.78