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Income Taxes (Narrative) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Income Tax [Line Items]      
Operating loss carryforwards $ 5,300 $ 5,300  
Net deferred tax asset 400 400  
Tax credit carryforwards $ 3,918 $ 3,512  
Provision for income taxes 22.50% 19.90%  
Unrecognized tax benefits $ 9,275 $ 9,251 $ 9,314
Unrecognized tax benefits that would impact the effective tax rate 9,100 9,100  
Interest and penalties included in income tax expense 1,800 300  
Accrued interest and penalties related to uncertain tax positions 3,400 1,600  
Total unrecognized tax benefits including interest 12,700 10,900  
Unrecognized tax benefits affected by the resolution of tax examinations or expiring statutes of limitation 400    
Income taxes receivable 1,100 5,000  
Foreign Tax Authority      
Income Tax [Line Items]      
Tax credit carryforwards $ 3,600 $ 3,300