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Directions: Solve the following linear diophantine equations. 1. x2 + 2y- = zz 2. x2 - 2y2 = z2 3. x2 + y2 = 2z2

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Directions: Solve the following linear diophantine equations. 1. x2 + 2y- = zz 2. x2 - 2y2 = z2 3. x2 + y2 = 2z2 4. x2 - y2 = 3 5. 7404x + 7032y = 36 6. Do integer solutions to 2x + 3y = 0 exist? If so, find one. If not, explain why not. 7. 10x + 15y = 1 has no solutions. What is the essential reason

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