S saha.subham Jul 2009 68 0 May 18, 2010 #1 prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely.

prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely.

K kompik Mar 2010 116 41 Bratislava May 19, 2010 #2 saha.subham said: prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely. Click to expand... This one is easy. \(\displaystyle 6q+5=3(2q+1)+2\). The number 2 is the counterexample needed in the second part. Reactions: saha.subham

saha.subham said: prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely. Click to expand... This one is easy. \(\displaystyle 6q+5=3(2q+1)+2\). The number 2 is the counterexample needed in the second part.

K kompik Mar 2010 116 41 Bratislava May 19, 2010 #4 saha.subham said: plzz explain a bit more the part two Click to expand... 2=3.0+2, so it is of the form 3q+2 (take q=0). 2 is not of the form 6q+5. If it were, then 2=6q+5 3=6q q=-1/2, which is not an integer. Reactions: saha.subham

saha.subham said: plzz explain a bit more the part two Click to expand... 2=3.0+2, so it is of the form 3q+2 (take q=0). 2 is not of the form 6q+5. If it were, then 2=6q+5 3=6q q=-1/2, which is not an integer.