Question

show that any positive odd integer is of the form 6M + 1 or 16 + 3 or 6 m + 5 Where M is some integer

Answer 1

let x be an integer of the form 6m,6m+1,6m+2,6m+3,6m+4,6m+5

out of these 6m,6m+2,6m+4 are even integers..


so 6M + 1 or 6 m+ 3 or 6 m + 5 are odd integers..


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Answer 2

Let x be the positive integer.
By Euclid's divison lemma.
a= bq + r
Here putting b = 6 and r = 1,2,3,4,5,
Then,integers will be

x=6q+1
x=6q+2
x=6q+3
x=6q+4
x=6q+5
Here, 6q+2 and 6q+4 are the even positive integers.
Therefore, 6q+1,6q+3 and 6q+5 are the odd positive integers.
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