joesephhardaway3823 joesephhardaway3823
  • 29-08-2019
  • Mathematics
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Question 2. Solve the Diophantine equations: (2.a) 21x + 15y = 61 (2.b) 22u + 150 = 6

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sqdancefan
sqdancefan sqdancefan
  • 02-09-2019

Answer:

  no solution (either equation)

Step-by-step explanation:

2.a  21x +15y = 61 . . . . has no solution in integers

The left side is a multiple of 3; the right side is prime. No multiple of 3 will be a prime number.

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2.b subtracting 6 from both sides and dividing by 2 gives ...

  11u +72 = 0

72 is not a multiple of 11, so there can be no integer value of u that satisfies this equation.

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Neither equation has an integer solution.

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