Question:

A pair of positive integers $(x, y)$ satisfies the equation $4x - 17y = 1$. x also satisfies the inequality $x \leq 1$. Find the number of pairs $(x, y)$ that will satisfy the above?

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In Diophantine equations, always check the range of values that satisfy both the equation and any additional constraints.
Updated On: Aug 5, 2025
  • 59
  • 57
  • 55
  • 58
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The Correct Option is D

Solution and Explanation

We solve the Diophantine equation $4x - 17y = 1$ and find the integer solutions for $x$ and $y$. By applying the inequality condition $x \leq 1$, we get the total number of valid pairs as 58.
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