Word Count : 476

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We are asked to solve $5^x \equiv 22 \pmod{47}$ using the Baby-Step Giant-Step algorithm. --- Step 1: Identify parameters The modulus is $p = 47$, a prime. The base is $g = 5$. We want to solve $5^x \equiv 22 \pmod{47}$. Let $m = \lceil \sqrt{p-1} \rceil = \lceil \sqrt{46} \rceil = 7$. We will compute: * Baby steps: $g^j \mod p$ for $j = 0, 1, \dots, m-1$ * Giant steps: $h \cdot g^{-im} \mod p$ for $i __________ ____ ____ __________ _________ _____ _______ _____ _________ ____ ____ _____.
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