Question

hi

show that any positive integer is of the form


6q,6q+1,6q+2,6q+3,6q+4,6q+5

Answer 1

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$\huge{ \mathfrak{ \blue{here \: is \: answer}}}$

let a be any positive integer

then

b= 6

a= bq+r

0≤r<b

0≤r<6

r= 0,1,2,3,4,5

case 1.

r=0

a= bq+r

6q+0

6q

case 2.

r=1

a= 6q+1

6q+1

case3.

r=2

a=6q+2

case 4.

r=3

a=6q+3

case 5

r=4

a=6q+4

case 6..

r=5

a=6q+5

hence from above it is proved that any positive integer is of the form 6q, 6q+1,6q+2,6q+3,6q+4 and 6q+5and

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Answer 2

solutions :-

Let m be any positive integer

b = 6

a = bq+r

0≤r<b

0≤r<6

r = 0,1,2,3,4,5

case 1:-

r = 0

= bq+r

6q+0

6q

case 2:-

r = 1

m= 6q+1

case 3:-

r = 2

m=6q+2

case 4:-

r = 3

m=6q+3

case 5:-

r = 4

m=6q+4

case 6 :-

r = 5

m=6q+5

Hence

it is proved that any positive integer is of the form 6q, 6q+1,6q+2,6q+3,6q+4 and 6q+5

Thanks

@Anushka