Question

show that any positive odd integer is in the form of 6q+1,6q+3,6q+5 where q is an integer

Answer 1

this is your answer....

Answer 2

Heya!

Here is yr answer.....


Let a is any positive integer, b = 6

According to Euclid's postulate.....

a = bq + r [ 0<r< / = b]

a = 6q + r [ 0<r< / = 6]



Possible values of r = 1,2,3,4,5


r = 1 => 6q+1

r= 2 => 6q+2

r = 3 => 6q+3

r = 4 => 6q + 4

r = 5 => 6q + 5


Here,

6q+2 , 6q+4 are divisible by 2 .So they are even integers.

6q+1, 6q+3 ,6q+5 are odd integers

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


Hope it hlpz....