+4622 Find the largest negative integer x which satisfies the congruence \(34x+6\equiv 2\pmod {20}\).
+9673 If 34x + 6 congruent 2 mod 20, 34x + 4 is divisible by 20.
We use trial and error(again) and test for each negative integer from -1.
34(-1) + 4 = -30 which is not divisible by 20.
34(-2) + 4 = -60<-- OMG answer already here. It is divisible by 20.
Therefore the largest negative integer which satisfies the congruence is -2 :)
~The smartest cookie in the world.
+26393 Find the largest negative integer x which satisfies the congruence
\( 34x+6\equiv 2\pmod {20}\).
\(x = -6+10n \quad | \quad n \in \mathbb{Z}\)
The largest negative integer x = - 6
Check:
\(\begin{array}{|rcll|} \hline && 34\cdot(-6)+6 \pmod {20} \\ &\equiv & -204 + 6 \pmod {20} \\ &\equiv & -198 \pmod {20} \\ &\equiv & -18 \pmod {20} \\ &\equiv & -18+20 \pmod {20} \\ &\equiv & 2 \pmod {20} \\ \hline \end{array}\)
