1. Use the extended Euclidean algorithm to solve the following linear congruence: 11111x \equiv 4 \pmod{12345}
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\[ \begin{array}{rcl} 12345 & = & 11111 \cdot 1 + 1234 \\ 11111 & = & 1234 \cdot 9 + 5 \\ 1234 & = & 5 \cdot 246 + 4 \\ 5 & = & 4 \cdot 1 + 1 \\ 4 & = & 1 \cdot 4 + 0 \\ \end{array} \] The gcd is 1. Show more…
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