Question

Show that any positive odd integers is of the form 6m+1,6m+3,6m+5 for some integers m

Answer 1

Answer:

prove . Any positive integers can be write in the form of 6m+1,6m+3,6m+5 for some integers m.

Step-by-step explanation:

6m+1, 6m+3, 6m+5

here, let a and b are two positive integers , where b is 6. r is remender 1,2,3,4,5. less then 6.

so we use Eculid division lemma

a=bq+r

Dividend = Divisors ×quotiont + remender

a = bq + r

a = 6q + 1 = 2(3)q +1 odd

a = 6q + 2 = 2(3q+1) odd

a = 6q + 3 = 3(2q+1) even

a = 6q + 4 = 2(3q+2)even

a. = 6q + 5 = 2(3q) +5 odd

so ,we can say all the positive integers can be written in the form of 6q+1, 6q+3, 6q+5 , the square of an odd integers can be of the form 6m+1,6m+3,6m+5 for some integers m .

I hope you satisfied for answer.

⭐⭐ Rohan kumar

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