Question

show that any positive odd integer is of the form 6q+1, or 6q+3,or 6q+5,Where q is some integer​

Answer 1

Answer:

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Step-by-step explanation:

Let a be a given integer.

On dividing a by 6 , we get q as the quotient and r as the remainder such that

a = 6q + r, r = 0,1,2,3,4,5

when r=0

a = 6q,even no

when r=1

a = 6q + 1, odd no

when r=2

a = 6q + 2, even no

when r = 3

a=6q + 3,odd no

when r=4

a=6q + 4,even no

when r=5,

a= 6q + 5 , odd no

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

Answer 2

Step-by-step explanation:

let us assume the integer be x and b = 6

we use formula here a = bq + r

x = 6q + r where r = 0 < r < 6

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

for r = 0

x = 6q + 0

x = 6q

for r = 1

x = 6q + 1

for r = 2

x = 6q + 2

x = 2(3q + 1 )

for r = 3

x = 6q + 3

x = 3 ( 2q + 1)

for r = 4

x = 6q + 4

x = 2 (3q + 2 )

for r = 5

x = 6q + 5

a = 6q, 6q + 2 , 6q + 4 are positive even number

a = 6q + 1, 6q + 3 , 6q + 5 are odd integer for a is q

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