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Income Taxes (Schedule of Effective Income Tax Rate Reconciliation) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 31, 2023 | Aug. 31, 2022 | Aug. 31, 2021
Income Tax Disclosure [Abstract] |  |  |
Amount computed at U.S. statutory federal tax rate | $ 17,884 | $ 17,662 | $ 18,165
Effect of foreign operations | 1,583 | 317 | 629
Net benefit from GILTI/FDII | (2,071) | (2,002) | (1,764)
Expense (benefit) from stock compensation | 538 | (204) | (1,813)
Uncertain tax positions and related interest | 1,377 | 273 | 222
Other | (141) | 733 | 831
Provision for income taxes | $ 19,170 | $ 16,779 | $ 16,270

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