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📰 Question: How many lattice points lie on the hyperbola defined by the equation $x^2 - y^2 = 2025$? 📰 Solution: The equation $x^2 - y^2 = 2025$ factors as $(x - y)(x + y) = 2025$. Since $x$ and $y$ are integers, both $x - y$ and $x + y$ must be integers. Let $a = x - y$ and $b = x + y$, so $ab = 2025$. Then $x = \frac{a + b}{2}$ and $y = \frac{b - a}{2}$. For $x$ and $y$ to be integers, $a + b$ and $b - a$ must both be even, so $a$ and $b$ must have the same parity. 📰 We factor $2025 = 3^4 \cdot 5^2$, so the number of positive divisors is $(4+1)(2+1) = 15$. Each divisor pair $(a, b)$ corresponds to a solution, and since $a$ and $b$ must have the same parity, we count such pairs. 📰 Best Diffuser For Curly Hair 761647 📰 Sudden Decision Wizard Of Oz Slots Free Coins And The Crisis Deepens 📰 Transform Your Netsuite Knowledge Mylearn Module Secrets Revealed 9337688 📰 Car Insurance Online Quotes 📰 Bank Of America B Of A 📰 Fionnas Rise To Fame Is She The Next Big Thing Find Out 185255 📰 From Venezuela To Your Tablewhat Casabe Does For Immunity Is Shocking Hint Its All About Gut Health 1834985 📰 Trezor Review The Cool Device Taking Crypto Security By Storm 1031798 📰 How To Join A Group In Roblox 📰 Red Ghost Marvel The Unbelievable Power Behind This Hidden Phenomenon 7410561 📰 Saint Petersburg Fl Time 1063374 📰 Major Gainers Today 📰 Lord Of The Rings Pc Games 📰 Weather In Tokyo Dec 1899839 📰 Get Shockwave Player 524877