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📰 oxed{i}Question: What is the smallest positive integer whose cube ends in the digits $888$? 📰 Solution: We seek the smallest positive integer $ n $ such that $ n^3 \equiv 888 \pmod{1000} $. This means we want the last three digits of $ n^3 $ to be $888$. We solve this congruence modulo $1000$. Since $1000 = 8 imes 125$, and $8$ and $125$ are coprime, we can use the Chinese Remainder Theorem by solving modulo $8$ and modulo $125$ separately. 📰 First, modulo $8$: 📰 Heat Of Vaporization 9326377 📰 How Old Is Jeff Probst 6935994 📰 Microsoft Essential Antivirus For Windows 7 284971 📰 Nyse Nke Financials Leak What This Means For Investors And The Broader Market Today 3446274 📰 Transform Your Look Instantlybuff Rub Proven To Work Like Magic Try It Now 7660555 📰 Grow More With These Shrubs Hidden Among Your Rosesdont Miss These Landscape Stars 1051550 📰 Film Seeking A Friend For The End Of The World 6297422 📰 Shows On Netflix 6062411 📰 Access Real Surgeries Through Gamessurgical Simulations That Debut Online 9666527 📰 Bank Of Login 6407184 📰 Celebrities Who Lost Homes In Fire 2025 688458 📰 Airtel Recharge 6042092 📰 Vrssd Stock 417437 📰 Dr Alan Helps Students Build A Solar Powered Robot Each Robot Needs 5 Solar Panels And 3 Microcontrollers If He Buys 140 Solar Panels And 80 Microcontrollers What Is The Maximum Number Of Complete Robots They Can Build 6036091 📰 Call Me Tonethis Hidden Motto Bends How You Speak And Transforms Everything You Say 8113811