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:

answer is in attachment...

Answer 2

Answer:

Let a be a given integer.

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such that

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd nowhen r=4

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd nowhen r=4a=6q + 4,even no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd nowhen r=4a=6q + 4,even nowhen r=5,

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd nowhen r=4a=6q + 4,even nowhen r=5,a= 6q + 5 , odd no

Let a be a given integer.On dividing a by 6 , we get q as the quotient and r as the remainder such thata = 6q + r, r = 0,1,2,3,4,5when r=0a = 6q,even nowhen r=1a = 6q + 1, odd nowhen r=2a = 6q + 2, even nowhen r = 3a=6q + 3,odd nowhen r=4a=6q + 4,even nowhen r=5,a= 6q + 5 , odd noAny positive odd integer is of the form 6q+1,6q+3 or 6q+5.

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