Linear Diophantine Equation/Examples/15x + 27y = 1
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Example of Linear Diophantine Equation
The linear diophantine equation:
- $15 x + 27 y = 1$
has no solutions for $x$ and $y$ integers.
Proof
We have that:
- $\gcd \set {15, 27} = 3$
which is not a divisor of $1$.
So, from Solution of Linear Diophantine Equation, no solution exists.
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-3}$ The Linear Diophantine Equation: Example $\text {2-12}$