Yao Chen
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 Sep 27 awarded Commentator Sep 12 awarded Student Sep 12 awarded Scholar Sep 12 accepted How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? @Rob: so 14 it is! thanks! Sep 12 awarded Supporter Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? @Rob, last question, is x=14 the ONLY solution, or is 14 the total number of solutions to 6x = 14 mod 35 in Z/35Z? Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? so then there would 34 solutions to this problem? since all those numbers mod 35 is 14!? Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? @Rob: if x 34, then 6x = 204, how is 204 = 14 % 35? since 14%35 is 14?! sorry, im very confused. Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? so the solution to Z/35Z should be {14+35n | n ∈ Z35}? from what i remember from class, Z/35Z = {0..34}, so i should only compute this up to n = 34? Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? "14,14+35,14+2⋅35…" how high does this go? up to 14+35*35?
14+35= 49, 49%35 = 14 also... so from this, the possible solutions are (14,49,84,119,154,189,224,259,294,329,364,399,434,469,504,539,574,609,644,679,71‌​4,749,784,819,854,889,924,959,994,1029,1064,1099,1134,1169) i wrote a python code to run up to 35.. do i go over 35 or it should be {0..34} since it is Z/35Z? Sep 12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? correct me if im wrong, so we have that 14mod35 = 14, and 84 is a solution because 84%35 = 14? how do i find other solutions to this problem? i edited the question. please take a look. thank you!
since 14%35 = 14 in Z35, then wouldnt there be an infinite number of solutions? since there tons of numbers that mod 35 is 14?! Sep 12 awarded Editor Sep 12 revised How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? edited title Sep 12 revised How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? edited tags Sep 12 asked How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have?