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\title{Math 184 Homework 1}
\date{Fall 2022}
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This homework is due on gradescope Friday September 30th at 11:59pm pacific time. Remember to justify your work even if the problem does not explicitly say so. Writing your solutions in \LaTeX is recommend though not required.
\begin{ques}[Ackermann Function, 50 points]
The Ackermann function is a function $A(m,n)$ that takes as input two integers $m,n\geq 0$ and returns an integer. For all $n,m\geq 0$, it satisfies the recurrence relation:
\begin{eqnarray*}
A(0,n) & = & n+1\\
A(m+1,0) & = & A(m,1)\\
A(m+1,n+1) & = & A(m,A(m+1,n)).
\end{eqnarray*}
Prove that the above recurrence relations uniquely define the value of $A(m,n)$ for all integers $m,n\geq 0$. Hint: You will want to use induction, but you will need to be careful about what you are inducting on and how you set it up.
\end{ques}
\begin{ques}[Generalized Binary Representation, 50 points]
Let $a_1