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.
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Originally Posted by 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. This one is easy. $\displaystyle 6q+5=3(2q+1)+2$. The number 2 is the counterexample needed in the second part.
plzz explain a bit more the part two
Originally Posted by saha.subham 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.
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