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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 $8$: 📰 Css Profile College Board 4500498 📰 Discover The Forgotten Roles Of Women In The Bible That Shock Modern Readers 8991287 📰 7 Layer Cookies The Ultimate Treat Thats Too Good To Resistclick To See Why 8710440 📰 Stop Missing Big Dividendshere Are The Top Stocks Yielding Over 8 216344 📰 Never Guess What This Ancient Wood Reveals About Natures Power 773355 📰 Unlock The Shocking Transformation From 19C To F In One Breakneck Move 8656049 📰 Report Reveals Free Item Search Games And The Fallout Continues 📰 Struggling To Log Into Lake Michigan Credit Union We Found The Quick Fix Youve Been Hunting 5347387 📰 Wells Fargo Bank Golden Valley Mn 📰 Honor Your Troopmicrosoft 365 Military Appreciation Edition Delivers Family Friendly Perks Now 682186 📰 Strip 2452085 📰 In Steal A Brainrot In Roblox 📰 Cheapest Insurance Auto 📰 Nyse Financials Secrets Revealed Is Your Portfolio Exposed To Billion Dollar Gains 7105297 📰 Unsecured Credit Cards For Bad Credit