(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There's a couple of questions that require the use of this, I'm having trouble with one of them, could anyone help?

2. Relevant equations

a) 520x - 1001y = 13

b) 520x - 1001y = -26

c) 520x - 1001y = 1

3. The attempt at a solution

The first two are easy to do,

where you set 1001 and 520 as a and b respectively.

so:

1001 = 1*520 + 481

520 = 1*481 + 39

481 = 12*39 + 13

39 = 3*13 + 0 for a)

39 = 26 + 13 for b)

And you use back-substitution for the first two and change the signs accordingly, that's fine,

so you start with:

a) 13 = 481 - (12*39)

b) 26 = 39 - 13

c) 1 = ?

for c), I'm stumped. Do you use a fraction or something? or is there no solution? thanks for any help you can give me.

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# Extended Euclidean Algorithm

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