An exercise for the reader

March 15, 2026 math

Take the following two large numbers:

\begin{aligned} p &= 5213436955487338931744369 \\ q &= 72398891673349755598314 \end{aligned}

$(a)$ Apply the Euclidean algorithm to compute $\gcd(p,q)$ .
$(b)$ Let $q_0, q_1, \ldots, q_n$ denote the successive quotients obtained in $(a)$ . Determine $n$ .
$(c)$ Let $\Sigma$ denote the set of printable ASCII characters and let $f \colon \{0,\ldots,127\} \to \Sigma$ be the function mapping each integer to the character with that code point. Evaluate the string $f(q_0)\, f(q_1) \cdots f(q_n)$ .

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(f=(p,q)=>q?String.fromCharCode(Number(p/q))+f(q,p%q):'')(
  5213436955487338931744369n,72398891673349755598314n
)