Goodwill and Intangible Assets - Amortization (Details) - USD ($) $ in Thousands	3 Months Ended
Nov. 30, 2025	Nov. 30, 2024	Aug. 31, 2025
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization related to intangible assets	$ 152,447	$ 160,214
Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract]
Remainder of 2026	416,156
2027	494,448
2028	457,049
2029	365,208
2030	267,927
Thereafter	330,827
Net Carrying Amount	$ 2,331,615		$ 2,410,755

Finite-Lived Intangible Asset, Expected Amortization, After Year Four

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The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets.

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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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