Question

show that any positive odd integer is in the form of 4q+1 or 4q+3 where q is some integer

Answer 1

hey dear


here is your answer


Solution


Let we take A

where a is a positive odd integer

we apply division algorithm

a and b = 4


Since 0< r< 4

4q+1 or 4q + 2 or 4q + 3


where q is quotient


So

Since a is odd

a cannot be 4q or 4q + 2


they are both divisible by 2


Therefore any odd integer is of the form

4q + 1 or 4q + 3



hope it helps

thank you

Answer 2

Hi!!!!!

Here is yr answer _______________________________________________________

Let a is any positive integer and b=4 (a=bq+r)

So, 0<r<4

The possible remainders
4q ,4q+1,4q+2,4q+3

any positive odd integer will not be in the form of 4q, 4q+2.So,these are not possible.

Therefore,any positive odd integer is in the form of 4q+1 or 4q+3

Hope it hlpzzz.... ●_●

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