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/sci/ - Science & Math

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1190692 No.1190692 [Reply] [Original]

Alright, this is driving me crazy /sci/.

Equation of this gender; ax + by = 1 where (x,y) belongs to Z and a^b = 1 (coprime) has one solution or more according to Bachet-Bézout.

Implying that ax + by = c has also one solution at least.

15x - 32y = 1 -> How to find a solution?

>> No.1190711

http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm

>> No.1190752

Yeah, I'm using that and didin't get to a solution, did you?

>> No.1190756

>>1190752
yup

>> No.1190774

SHOW

>> No.1190779

>>1190774
1 = 15 * 15 - 7 * 32

>> No.1190793

>>1190692
>Implying that ax + by = c has also one solution at least.

>> No.1190827
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1190827

Even wrote the steps for you
32 = 32 * 1 + 15 * 0
15 = 32 * 0 + 15 * 1
2 = 32 * 1 + 15 * -2
1 = 32 * -7 + 15 * 15