Solving Modular Equations With Identities

Question

$4+2x≡7 \pmod 8$ Find all possible solutions and note any identities. Identify how you found the solutions. Explain what identities are.

score 2 · Accepted Answer · answered May 21 '13 at 08:22

2

$\implies 2x\equiv3\pmod 8=3+8a$ for some integer $a$

So, as $3+8a$ is odd and $2x$ is even for integer $x,$ there is no solution

More generally, using Linear congruence theorem (Proof) $ax\equiv b\pmod n$ is solvable iff $(a,n)$ divides $b$

answered May 21 '13 at 08:22

lab bhattacharjee

Thank-you, but I'm not exactly sure how that answers my question... I mean, it does indirectly... Directly, it leaves me wondering. Would you mind explaining it in regards to my question please? – Shayna May 21 '13 at 09:01
@Shayna, Please have a look into http://math.stackexchange.com/questions/372515/solve-for-x-4x-6-mod-5 – lab bhattacharjee May 21 '13 at 09:57
Ah, thank-you very much! It is a lot clearer now. I sat trying to solve that problem for quite some time. I didn't think my professor would be evil enough to give a problem with no solution! – Shayna May 21 '13 at 10:11

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