Question

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

Answer 1

Answer:

we need to find out odd integer.

Step-by-step explanation:

so,

r=0,1,2,3

q=some integer

a=bq+r

b=4

a=4q+1(because one is odd number in our remainder)

a=4q+3

thanks

Answer 2

Explanation :-

According to Euclid Divison Lemma,

↪If a and b are 2 positive integers, so

↪a = bq + r

↪[ Where, $0 \leq \: r \: < b$ ]

↪Let positive integers be b, so

↪b = 4

↪a = 4q + r

↪[ Where, $0 \leq \: r \: < 4$ ]

↪r is a integer greater than or equal to 0 and less than 4 .

↪.°. r = 0,1,2,3

↪If r = 1 ,

↪a = 4q + 1

[ This will always be an odd integers. ]

↪If r = 3 ,

↪a = 4q + 3

[ This will always be an odd integers. ]

Therefore, any odd integers is of the form, 4q + 1 or 4q + 3.

Hence Proved!!