Originally Posted by

**Melody2** Hello again,

My question concerns the Diophantine equation solution.

I can follow HallsofIvy's solution, at least at a very superficial level, but, firstly, I don't understand why it is more general and, secondly, I can't work out how to apply it to other problems.

I am considering

5/286 = x (mod7)

5=286x (mod7)

286/7 = 40 and 6/7 therefore 286 mod7 = 6

6x=5 mod7

6x = 5, 12,19 etc

x=2+7N where N is any integer

ok that's the easy way done with.

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now for the other way.

286x = 7y+5 for some y in the set of integers

286x-7y=5

286/7 = 40 +6/7

286=40(7)+6

286-40(7)=6 (1)

7/6 = 1 +1/6

7 = 6(1) +1

Sub in (1)

7 = 286-40(7) +1

-286+41(7) = 1

286(-1)-7(-41) =1

how does this help???

I'm obviously doing it wrong.

So my 2 questions are

What am I doing wrong and why is this way more general?

Thank you for your patience and your time.