use division algorithm to show that any positive integer is of the form 6q+1,6q+3,6q+5, where q is an integer
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Answer:
Step-by-step explanation:
let n be the positive odd integer
on dividing n by q let r be the remainder
by Euclid's division lemma n=6q+r, where r is 0,1,2,3,4,5
case 1, where r is 0
n=6q
case 2, where r is 1
n=6q+1
case 3, where r is 2
n=6q+2
case 4 where r is 3
n=6q+3
case 5 , where r is 4
n=6q+4
case 6, where r is 5
n=6q+5
clearly in case 2,4 and 6 it is odd
hence any +ve odd integer is in the form of 6q+1 , 6q+3 and 6q+5
HOPE THIS IS HELPFUL..............
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