# real number problem 2

#### saha.subham

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.

#### kompik

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.
This one is easy.
$$\displaystyle 6q+5=3(2q+1)+2$$.

The number 2 is the counterexample needed in the second part.

saha.subham

#### saha.subham

plzz explain a bit more the part two

#### kompik

plzz explain a bit more the part two
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.

saha.subham
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