Find the largest negative integer x which satisfies the congruence \(34x+6\equiv 2\pmod {20}\).

tertre
Mar 23, 2017

#1**0 **

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.

MaxWong
Mar 23, 2017

#5**+2 **

**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:

\(\begin{array}{|rcll|} \hline && 34\cdot(-6)+6 \pmod {20} \\ &\equiv & -204 + 6 \pmod {20} \\ &\equiv & -198 \pmod {20} \\ &\equiv & -18 \pmod {20} \\ &\equiv & -18+20 \pmod {20} \\ &\equiv & 2 \pmod {20} \\ \hline \end{array}\)

heureka
Mar 24, 2017