Word Count : 553

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We are given a discrete logarithm problem: $$ 5^x \equiv 22 \pmod{47} $$ We need to solve for $x$ using the Baby-Step Giant-Step (BSGS) algorithm manually. --- ### ✅ Step-by-step: Baby-Step Giant-Step This method is used to solve $a^x \equiv b \pmod{p}$. Here: * $a = 5$ * $b = 22$ * $p = 47$ --- ### Step 1: Compute m = ⌈√p⌉ $$ m = \lceil \sqrt{47} \rceil = \lceil 6.86 \rceil = 7 $$ --- ### Step 2: Compute baby steps (i.e., $a^j \mod p$ for $j = 0$ to $m-1$) We compute $5^j \mod 47$ for $j = 0$ to 6: | j | $5^j \mod 47$ ____ __________ _________ ____ _______ ____ _________ ____ _______ _____ ___.
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