Show that any positive odd integer is of the form 69 +1, or 69 +3, or 69 +5, where q is some integer.
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Let
′
a
′
be any positive integer and b=6
Then by division algorithm
a=6q+r where r=0,1,2,3,4,5
so, a is of the form 6q or 6q+1 or 6q+2 or 6q+3 or
6q+3 or 6q+4 or 6q+5
Therefore If s is an odd integer
Then
′
a
′
is of the form 6q+1 or 6q+3 6q+5
Hence a positive odd integer is of the form 6q+1 or 6q+3 or 6q+5
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