Linear Diophantine Equation/Examples/17x + 15y = 143/Historical Note

Historical Note on Linear Diophantine Equation: $17 x + 15 y = 143$

This exercise was originally couched in the language of a person making a purchase of:

$x$ items of commodity $A$, costing $17$ monetary units each

and:

$y$ items of commodity $B$, costing $15$ monetary units each

for a total outlay of $143$ monetary units.

It is apparent in this context that both $x$ and $y$ must be non-negative, and (in the specific wording of the question) can be interpreted as actually strictly positive.

Such exercises are usually (as this one is) specifically crafted so as to allow for only one solution.

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-3}$ The Linear Diophantine Equation: Exercise $2$