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Solution of a Single Linear Equation in Two Variables

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Question

Find the greatest value of $c$ in order that the equation $14 x + 11 y = c$ may have exactly five solutions in positive integers.

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Solution

The greatest value of $c = (n + 1) a b - a - b = 6 \times 14 \times 11 - 14 - 11 = 899$
Here, $n =$ no of solutions
$a$ and $b$ are coefficents of $x$ and $y$ respectively

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