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

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

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Let a be any positive integer
a=6q+r where 0 < or = r < 6
put r=1:

a=6q+1

which is an odd integer
r=3:

a=6q+3

which is an odd integer
r=5:

a=6q+5

which is an odd integer
therefore, any positive odd integer is of form 6q+1,6q+3 or 6q+5, where q is some integer.

 

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