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Show that any positive odd intger is of the form 6q+1,or 6q+3,or 6q+5 where q is some integer

Posted by Harshit Pandey Pandey 7 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Radhika :) Mishra:} 7 years, 8 months ago

0<r<6 so possible remainder are 1 2 3 4 5 then by applying r=1we have 6q+1 now applying r=2 we have 6q+2 now applying r=3 we have 6q+3 now applying r=4 we have 6q +4 and lastly applying r =5. We have 6q+5 so we have all the above equations

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Prakash Mishra 7 years, 8 months ago

Let n be a given positive odd integer . On dividing n by 6 , let m be the quotient and r be the reminder Then by Euclid division lemma ,we have n =6m+r where 0<and equal r <6 = , n= 6m+r where r= 0,1,2,3,4,5 = n=6m or (6m+1)(6m+2) (6m+3) 6m+4) (6m+5) But n= 6m , 6m+2 ,6m+4 given even value of n Thus ,when n is odd , it is of the form 6m+1 ,6m+3 or 6m+5 for some integer m

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