The question asks to solve for $b$ in the following equation: $2^b \equiv 893 \pmod{1373}$ However I am not sure how to solve this, as I only know how to solve for integers on the left hand side. The solution indicates that $b = 219$.
2026-02-23 02:56:51.1771815411
Solve for $b$ in the equation $2^b \equiv 893 \pmod{1373}$
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Finding $b$ from this equation is a discrete logarithm problem in $\mathbb{F}_{1373}$, a finite field. These do not have known fast algorithms (only subexponential ones) and for truely large parameters take a long time to solve. In this case $p-1 = 2^7 \cdot 7^3$ and so we do have a relatively fast algorithm ($p-1$ is smooth).
But I don't know what algorithms/theory is covered in your course, and in this case a trivial Python script will give you the answer $(219$ indeed) in less than a second anyway. The paramaters are quite small.