plshelp111
New member
- Joined
- Aug 15, 2020
- Messages
- 5
Hello,
(= , congruence)
So ax = b (mod m) has 1 answer when gcd(a,m)=1|b . My question is why, for example with 2x = 3 (mod 5) the only aswer is x = 4 (mod 5) when x = 9 (mod 5) also works (I assume that 0<= x < m but why? And why not 4+5k?). I learned to solve such equations with the 'inverse of a modulo m', so gcd(a,m) = ua + vm thereby x = u*b (mod m) but applying this to the above question I get: gcd(2-5+2*2, 5-2*2)=1 or gcd(2, 5) = -2a + m = -2 * 2 + 5, which gets us x= -2*3 (mod 5). Which does not equal 4 (mod 5), or do they mean ( not a congruence) x = 4 = (-6 mod 5) ?
As you see I'm really confused and any help is appreciated.
Kind regards,
A.A.
(= , congruence)
So ax = b (mod m) has 1 answer when gcd(a,m)=1|b . My question is why, for example with 2x = 3 (mod 5) the only aswer is x = 4 (mod 5) when x = 9 (mod 5) also works (I assume that 0<= x < m but why? And why not 4+5k?). I learned to solve such equations with the 'inverse of a modulo m', so gcd(a,m) = ua + vm thereby x = u*b (mod m) but applying this to the above question I get: gcd(2-5+2*2, 5-2*2)=1 or gcd(2, 5) = -2a + m = -2 * 2 + 5, which gets us x= -2*3 (mod 5). Which does not equal 4 (mod 5), or do they mean ( not a congruence) x = 4 = (-6 mod 5) ?
As you see I'm really confused and any help is appreciated.
Kind regards,
A.A.