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Stockholders' Equity (Restricted Stock and SARS Information) (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2020
Aug. 31, 2019
Aug. 31, 2018
Share-based Payment Arrangement [Abstract]      
Intrinsic value of SARS exercised $ 2,329 $ 335 $ 909
Fair value of restricted stock units vested 55,799 49,725 62,592
Tax benefit for stock compensation expense 1,159 $ 611 $ 1,122
Unrecognized stock-based compensation expense — restricted stock units $ 38,909    
Remaining weighted-average period for restricted stock units expense 1 year 3 months 18 days