Question

B) show that any positive odd integer is of the form 4q+1 or 4q+3, where „q‟ is some integer

Answer 1

Here your answer goes

Euclid Division Lemma :-  

• It is basically a theorem given be Euclid
• In this  Division lemma Divisior = Dividend * Quotient + Remainder
• a = bq + r
• Where , 0 $\leq$ r ∠ b

The proof of your question as below :-

Step :- 1

Let a be any positive integer

b = 4

Step :- 2

a = bq + r

a = 4q + r----->> 1

Where ,

Where , 0 $\leq$ r ∠ b

Where , 0 $\leq$ r ∠ 4

Step :- 3

Put r = 1 , 3

a = 4q + 1

a = 4q + 3

⊂⊂⊂⊂⊂⊂⊂⊃⊃⊃⊃⊃↓↓↓

Be Brainly

Together we go far →→→

Answer 2

Let a be the positive odd integer b=4

according to Euclid's division lemma

a=bq+r

a=4q+r

where , a=0,1,2,3

then,

a=4q

or

a=4q+1

or

a=4q+2

or

a=4q+3

a=4q+1 & a=4q+3 are odd

@skb