AMC 10 Daily Practice - Diophantine Equations

Complete problem set with solutions and individual problem pages

Problem 1 Medium

How many positive integer solutions of the following diophantine equations: 3x+8y=25 are there?

  • A.

    0

  • B.

    1

  • C.

    2

  • D.

    3

Answer:B

\begin{cases}x=3 \\ y=2 \\ \end{cases}

8y < 25, y \leqslant 3. y = 1, 2 \text{ or } 3. Plug in and solve for x, we have x = 3, y = 2.

Related Problems
Problem 2 AMC 10 Daily Practice - Diophantine Equations
Problem 3 AMC 10 Daily Practice - Diophantine Equations
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