Question

Show that positive integer of the form or 6q +1 or 6q+3 or 6q +5 where as q is some integer

Answer 1

Here your answer goes

Step :-1

Let a be positive integer

b = 6

a = bq + r

$0 \leq$ r ∠ b

Step :- 2

a = 6q + r

$0 \leq$ r∠ b

Step :- 3

Put  r = 1 , 3 , 5

a = 6q + 1

a = 6q + 3

a = 6q + 5

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Answer 2

Let a be the positive odd integer b=6

according to Euclid's division lemma

a=bq+r

a=6q+r

where a=0,1,2,3,4,5

then

a=6q or a=6q+1 or a=6q+2 or a=6q+3 or a=6q+4 or a=6q+5

Here

a=6q+1 & a=6q+3 & a=6q+5 are odd

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