## mwgc 3 years ago linear congruence: complete soln: 4x(is equivalent to) 5(mod 21) @Mathematics

1. bluebrandon

when I did the EEA I got 4(-5) + 21(1) = 1

2. mwgc

but then you have to mult by 5

3. mwgc

then x=xnot+bn/d

4. bluebrandon

when I multiplied by 5 I got 4(-25) + 21(5) = 5

5. mwgc

o ya then xnot is -25

6. mwgc

x=-25+21n

7. bluebrandon

your way of writing things is different then how I did it

8. mwgc

you have to find all solutions

9. bluebrandon

yeah I got x is congruent to 17 (mod 21)

10. mwgc

k so where do i go from here

11. bluebrandon

from the EEA you just convert it back into congruent form I think

12. mwgc

so x is congruent to -25 is congruent to what

13. bluebrandon

so 4(-25) congruent to 5 (mod 21) so x congruent to -25 (mod 21/1) is the complete solution and that is equivalent to x congruent to 17 (mod21/1

14. bluebrandon

since (-25) is some solution for x

15. bluebrandon

then you just put it into the Linear Congruence Theorem, V1

16. bluebrandon

to get the complete solution

17. mwgc

o crap ok now i see it

18. bluebrandon

I don't know this stuff super well either lol

19. mwgc

did you show eea?

20. bluebrandon

yeah I put it in there

21. mwgc

but theres no room

22. bluebrandon

the EEA for those were really short so I just wrote it in there tiny

23. bluebrandon

have you done any other problems on the assignment? I'm stuck on 5c lol

24. mwgc

only up to 3

25. bluebrandon

ok well I guess I might try asking on here again then

26. mwgc

metoo

27. mathTalk

4x(is equivalent to) 5(mod 21) 21 | 4x-5 21|4*(-4)-5 Hence -4 is a solution. ??? I am not sure.

28. mwgc

i dunno

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