Question

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

Answer 1

Answer:

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.

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Answer 2

QUESTION -

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

ANSWER -

Let a be any positive integer

a=6q+r where 0< or equal to r <6

put r=1: a=6q+1 =odd integer

r=3: a=6q+3=odd integer

r=5: a=6q+5=odd integer

therefore,any positive odd integer is of the form 6q+1,6q+3 or 6q+5,where q is some integer.

@HarshPratapSingh