how to solve 7x+6 ≡ 3 mod 41 ?

Question

how to solve  7x+6 ≡ 3 mod 41 ?

amistre64 · Answer

mod 41 means that we count on a circle or repetition from 1 to 41

amistre64 · Answer

1 = 42
2 = 43
3 = 44
4 = 45
 etc

anonymous · Answer

what is x than?

amistre64 · Answer

0 = 41
1 = 42
2 = 43
3 = 44
4 = 45
 .      .
 .      .
 .      .
41 =82

amistre64 · Answer

depends, what doe 3 mod41 equal?

anonymous · Answer

it's 3 however, according to the definition of congruence, both 3 and 7x+1 should have the same remainder

amistre64 · Answer

good, but i think you meant 7x+6 right?  and 3 mod 41 = 44

7x + 6 = 44

7x = 38

x = 38/7   but im sure that you want an integer value

anonymous · Answer

the answer is x=23, check with wolframaplha

amistre64 · Answer

23 sounds reasonable yes :)

anonymous · Answer

anonymous · Answer

but how do I solve it, show me a suggestion

amistre64 · Answer

7(23) + 6

140+21+6

167 divided by 41 = 4 with a remainder of 3

which is how it looks when its is already solved

amistre64 · Answer

3 mod 41 means that the number is divisible by 41 and has a remainder of 3

anonymous · Answer

yeah..I know, but show me how to solve it with Euclides

amistre64 · Answer

with euclides?  i got no idea what that method would be

anonymous · Answer

ok, but thanks anyways

amistre64 · Answer

good luck :)