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📰 Since the sum $x + y + z$ modulo 7 is uniformly distributed over the 7 possible residues (0 through 6), and the cubes are symmetric and large, we expect the number of triples with each residue class to be approximately equal. 📰 So $k = 8m$, and $n = 125(8m) + 38 = 1000m + 38$. The smallest positive solution is $n = 38$. 📰 Question: A materials scientist is modeling the crystal lattice of a new self-healing polymer and finds that the number of atoms in a unit cell satisfies a number-theoretic condition: it is a three-digit number that is one less than a multiple of 11 and one more than a multiple of 13. What is the smallest such number? 📰 Windows Azure Backup Pricing Explodedis Your Business Paying Too Much Heres What You Need To Know 7983917 📰 Rachel Blakely 6948762 📰 6 Feet To Inches 3854114 📰 Powershell Scripts You Cant Ignore Game Changing Tools Everyone Needs 3797770 📰 Protagonist Therapeutics Stock 5242150 📰 Wells Fargo Brenham 2077786 📰 News Nj 9760435 📰 400Ml Equals How Many Cups The Rapid Conversion That Everyone Gets Wrong 5477191 📰 Breaking Egan Stock Is Surgingheres Why Millions Are Jumping On The Win Now 4684187 📰 Billy Warlock 8062910 📰 4C Hair Men Unlocked The Ultimate Guide To Rocking Curls Like A Pro Viral Now 5949485 📰 Kaiser Stock 5208264 📰 Cast Of Season 4 Of The Walking Dead 7755375 📰 When Does A Lunar Eclipse Take Place 7288752 📰 You Wont Believe How Many Harry Potter Movies Secretly Changed The Franchise 5915246