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

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​

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3 weeks 2021-11-07T09:08:57+00:00 2 Answers 0 views 0

1. Any number divided, can be written in the form of

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.

,

⟹ a = bq + 1

,

⟹ a= bq + 3

,

⟹ a = bq + 5.

______________________

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.

Hope it helps you.