Hello I have the following question.(adsbygoogle = window.adsbygoogle || []).push({});

----

Solve the following congruences simultaneously:

[tex]2x + 3y \equiv 2 mod 631[/tex]

[tex]3x + 2y \equiv 3 mod 631[/tex]

----

I first tried adding and got [tex]5x + 5y \equiv 5 mod 631[/tex], but I was then stuck, so I tried the old multiplication, which looked worse as: [tex]6x^2 + 13xy + 6y^2 \equiv 6 mod 631[/tex]

Any ideas? I am guessing that I need to go somewhere with the addition one, but I can't see where. The instructor had a hint of using the fact that 631 is prime, but I can't see anything from that. Thanks.

Hmm, just got an idea, [tex]5(x + y) \equiv 5 mod 631[/tex], then find inverse of 5 and multiply it through to find x+y = something mod 631. I did this and got:

[tex]x + y \equiv 5*79380 mod 631[/tex]

which is

[tex]x + y \equiv 1 mod 631[/tex]

Now where can I go from here? Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Congruence problem

**Physics Forums | Science Articles, Homework Help, Discussion**