I can't figure out how to solve the: $$s'*51+t'*39=gcd(51,39)$$
I solved:
$$s'*51+t'*39=gcd(51,39) \to 3=-3*51+4*39$$
Are there any couples of whole numbers $(s',t')$ that solves my problem?
Thanks in advance!
2026-03-30 10:38:16.1774867096
Congruence equation of 2 unknown numbers
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2x+ 3y= 7 has x= 2, y= 1 as solution. It also has x= 2+ 3k, y= 1- 2k as solutions, for k any integer. As I showed before, 2(2+ 3k)+ 3(1- 2k)= 4+ 6k+ 3- 6k= 7. Taking k= 1, x= 5, y= -1 is a solution: 2(5)+ 3(-1)= 10- 3= 7. Taking k= 2, x= 8, y= -3 is a solution: 2(8)+ 3(-3)= 16- 9= 7. Taking k= -1, x= -1, y= 3 is a solution: 2(-1)+ 3(3)= -2+ 9= 7.