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Income Taxes (Reconciliations of Unrecognized Tax Benefits) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 31, 2018 | Aug. 31, 2017 | Aug. 31, 2016
Reconciliation of Unrecognized Tax Benefits [Roll Forward] |  |  |
Beginning balance | $ 201,355 | $ 149,898 | $ 154,648
Additions for tax positions of prior years | 14,465 | 2,155 | 7,974
Reductions for tax positions of prior years | (21,045) | (12,233) | (20,045)
Additions for tax positions related to current year | 81,866 | 77,807 | 25,892
Cash settlements | (1,659) | (2,298) | (6,553)
Reductions from lapses in statutes of limitations | (7,496) | (10,446) | (7,099)
Reductions from settlements with taxing authorities | (5,928) | (6,061) | (1,787)
Foreign exchange rate adjustment | (4,853) | 2,533 | (3,132)
Ending balance | 256,705 | 201,355 | 149,898
Unrecognized tax benefits that would affect the effective tax rate (if recognized) | $ 117,455 | $ 75,223 | $ 72,152

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