Question

show that any postive odd positive interger is of the form bq+1 or bq+3 or bq+5 where q is same interger​

Answer 1

Answer:

Any odd integer is of the form bq+1 or bq +3 or bq +5.

Step-by-step explanation:

Let us start with taking a ,where a is a positive integer. We apply the division algorithm with a and b.

Since 0< r<b ,the possible reminder are 0,1,2,and 3.

That is ,a can be bq+1 or bq+3 or bq+5,where q is the quotient.

However ,since a is odd a can be bq+1 or bq+2 or bq+5.

Therefore any odd integer is of the form bq+1 or bq+3 or bq+5.

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Answer 2

Any number divided, can be written in the form of $\boxed{\sf{a = bq + r}}$

Where,

• a = divident
• b = divisor
• q = quotient
• r = remainder

“ a = bq + r ” where r = 0, 1, 2, 3, 4, 5.

But in the question it is mentioned positive odd integers, so r = 1, 3, 5.

$\sf{\red{When\:r=1}}$,

⟹ a = bq + 1

$\sf{\green{When\:r=3}}$,

⟹ a= bq + 3

$\sf{\blue{When\:r=5}}$,

⟹ a = bq + 5.

______________________

$\sf{Hence\:Proved!}$