sub: Connecting Discrete Mathematics and Computer Science

cs

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:Discrete Structures II

Number theory

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I am looking for a simple solutions.

I have a friend named Nikki, who's from New Zealand. Nikki and I went out to eat together, and I paid for both dinners. She was

going to pay me back, in cash$$but she had only New Zealand dollars $[$NZD$].($I was happy to take NZDs$.)$ Nikki had a giant supply

of $5$NZD bills; I had a giant supply of $5$ U$.$S$.$ dollar $[$USD$]$ bills. At the time, the exchange rate was $5NZD=3$USD $($or close

enough to $5$:$3$ for two friends to call it good$).$

$7\mathrm{.}62$ Prove that Nikki can pay me exactly $4$USD in value, through only the exchange of $5$NZD and $5$USD bills.

$7\mathrm{.}63$ In Exercise $7\mathrm{.}62,$ was there something special about the number $4?$ Identify for which nonnegative integers $x$ Nikki can pay me