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📰 Thus, the remainder is $\boxed{7}$. 📰 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. 📰 Light Blue Color Code 7274240 📰 Healthy Choice Frozen Meals 2415554 📰 Is The Sony Ps5 Price Increase A Hidden Cost Gamers Cant Ignore Proven Reasons 9254326 📰 Total A B 300 420 300420720720 3167903 📰 The Hidden Meaning Of Lucky Seven7 Unlock Hidden Fortunes Tonight 4238664 📰 Cl Share The Game Changer Everyones Talking About You Have To Try It 2334341 📰 Your Grades Are Hiding The Truththeyre Screaming Your Failures Before They Even Hit The Desk 4763890 📰 This Simple Word Toc Trick Will Cut Your Document Turnaround Time By 70 8351317 📰 Goddess Diana 8130129 📰 Youll Discover Unlike Any Other Gym Gamethis Ones Fire For Muscle Gains 266916 📰 Barbara Banda 9681045 📰 The Dreamy Headboard Youve Been Searching Forupholstered Excellence Backed By Milky Red Reviews 3168082 📰 Good Indoor Tv Aerial 1331593 📰 You Wont Believe What Lurks In Your Coffee After The Cat Poop Accident 8808818 📰 Microsoft Autoupdate On Mac 7322383