yao jiang
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 Sep27 awarded Commentator Sep12 awarded Student Sep12 awarded Scholar Sep12 accepted How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? Sep12 comment How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? @Rob: so 14 it is! thanks! Sep12 awarded Supporter Sep12 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? Sep12 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!? Sep12 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. Sep12 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? Sep12 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? Sep12 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?! Sep12 awarded Editor Sep12 revised How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? edited title Sep12 revised How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have? edited tags Sep12 asked How many solutions does equation $6x=14 \bmod 35$ in $\mathbb{Z}/35\mathbb{Z}$ have?