Question

Chalo genius ji meli maadat kar dhoo plssss mei aapki bahut bahut aabaari raahogi.......❤❤❤

I NEED 6TH ONE... PLSSS HELP ME GENIUS JI!!✌✌❤​

Answer 1

Heya!

Here is yr answer....


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let 'a' is any positive integer, and b = 6

According to Euclid's Postulate...

a = bq+r (0≤r<b)

a = 6q+r (0≤r<6)

Therefore, possible values of 'r' are 0,1,2,3,4,5


If,

r = 0 => a = 6q

r = 1 => a = 6q+1

r =2 => a = 6q+2

r =3 => a = 6q+3

r = 4 => a = 6q+4

r = 5 => a = 6q+5


Since, 6q, 6q+2 , 6q+4 are even integers and 6q+1 , 6q+3 and 6q+5 are odd integers..

Therefore, Any positive odd integer is of the form 6q+1 , 6q+3 or 6q+5


Hence proved!

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Hope it helps..

Answer 2

Answer is as follows :

Let 'a' be any positive integer and b = 6

According to Euclid's Division Algorithm :

a = bq + r (0>r>6)

Then

a = 6q + 1

a = 6q + 2

a = 6q + 3

a = 6q + 4

a = 6q + 5

Out of these 5 outcomes :

(6q + 1),(6q + 3) and (6q + 5) are odd integers.

(6q + 2),(6q + 4) are even integers.

So we conclude that

Any positive odd integer is of the form (6q + 1),(6q + 3) and (6q + 5) q is an integer.