Question

Use division algorithm to show that any positive odd integer is of the form of 6q+ 1 or 6q+3 or 6q +5 where q is some integer.

Answer 1

Answer:

let a be any positive integer b- 6

by euclid division algorithm a = bq+ r

b<r<0

6q ,6q+2 ,6q+4 is divisible by 2 hence its positive even integer.

hence 6q+1 ,6q + 3 ,6q+ 5 is odd integer .

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