Do whole numbers $x$ and $y$ exist so 61 can be written in the form $61=9x+15y$?
My book just covered Bezout's identity. How can I use it to find out if the coefficients exist?
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$\gcd(9,15) = 3$
Since $3$ does not divide $61$, no such numbers can be found.
Hint: The right hand side is always divisible by _____ no matter what integers $x$ and $y$ you pick.