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# Linear Diophantine Equations

What amounts of money can you make with only $5 and $7 bills? Can you make $23 with those 2 types of bills?

Yes or No?

Are there any non-negative integer solutions to the equation

\[ 13m + 15n = 170? \]

Yes or No?

If \( a>4 \) is an integer that is \( \color{red}{\text{not}} \) a multiple of 13, can we express \( 11a-39 \) as a non-negative integer linear combination of \( a \) and 13?

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