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Q2. Prove that ax + by = a + c is solvable if and only ifProgressQ1. Show that all solutions of 3x + 5y = 1 can be written inthe form x = 2 + 5t, y = -1 -3t;ax + by = c is solvable.Q3. Find all solutions in positive integers of 5x + 3y = 52.Q4. Prove that the Diophantine equation ax + by = c has asolution if and only if gcd(a, b) c. (5marks) |
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Answer» Answer: The CONDITION that the equation AX? +2hxy + by? +2GX +2fy+c=0, can take the form ax? +2hXY+bY? = by translating the ORIGIN to a suitable point is |
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