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📰 Let $d = \gcd(a,b)$. Then we can write $a = dx$, $b = dy$, where $\gcd(x,y) = 1$. Since $a + b = 1000$, we have: 📰 dx + dy = d(x + y) = 1000 \Rightarrow d \mid 1000 📰 So $d$ must be a divisor of 1000. Also, both $a$ and $b$ must be divisible by a perfect square greater than 1. Since $a = dx$ and $b = dy$, both $dx$ and $dy$ must be divisible by a square $s > 1$. That means $d$ must contain all the square factors of $s$, or at least $x$ and $y$ must together contain the square factors. 📰 500 Top Companies Fund 9193233 📰 5 Bf1 Battlefield Hackers Reveal How To Dominate Battles Like A Pro Today 9501130 📰 Reddits Hottest Square Circle Threads You Cant Miss Shocked By What Youll See 4080253 📰 You Wouldnt Believe The Power Of 46 Billion Won In Dollars 606414 📰 Watch What Ghosts Rise In Zombiu Zeme Like Never Before 8112311 📰 5 This Phun Stock Was Hidden For Yearsexperts Are Raving About Its Moment 3780280 📰 Hhs Structure 7712200 📰 Clay Electric Shocks The Worldyou Wont Believe What It Can Power 9269232 📰 Theyre Selling The Goods Yourselfcan You Prove Its Not Common Sense 487967 📰 Nc License Plates And Tags Agency 6609156 📰 Pika Labs Exposed The Truth The Mind Blowing Science Behind Their Shocking Launch 40946 📰 Cd Rates 14 Month 2893177 📰 Gleaming Slots Already Paying Big Winsheres How To Join The Fun Now 2186239 📰 Unlock The Secrets To Mastering Just Dance 2014Youll Never Not Believe How Fun It Is 8171781 📰 How To Determine Car Payment 447141