Goodwill and Intangible Assets - Amortization (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
May 31, 2025	May 31, 2024	May 31, 2025	May 31, 2024	Aug. 31, 2024
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization related to intangible assets	$ 153,199	$ 133,097	$ 465,575	$ 364,353
Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract]
Remainder of 2025	150,397		150,397
2026	563,620		563,620
2027	496,707		496,707
2028	459,216		459,216
2029	366,312		366,312
Thereafter	555,433		555,433
Net Carrying Amount	$ 2,591,685		$ 2,591,685		$ 2,904,031

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

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- Definition

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. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

+ References

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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).

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
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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 remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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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 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).

+ References

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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 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

+ Details

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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 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).

+ References

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- References

No definition available.

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- Definition

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

+ References

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- References

No definition available.

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