Let a and b two odd positive integers >1 and e = +1 or -1, is it true that...

...these propositions are equivalent :

1) a and b are co primes

2) there exist two odd positive integers, u<b, v<a such au-bv = 2e

3) there exist two odd positive integers, x<b, y<a such by-ax = 4e

For example

3 and 7 :

7-3 = 4

3.3-7 = 2

3 and 5 :

5-3 =2

3.3-5 = 4

5 and 7 :

7-5 = 2

5.5 - 7.3 = 4

11 and 15 :

15 - 11 = 4

11.7 - 15.5 = 2

7 and 17 :

7.3 - 17 = 4

17.3 - 7.7 = 2

Euzenius