ODD NUMBERS

ODD NUMBERS : 

 1  ,  3 ,  5,  7,  9, .... (2n+1)

When a number is divided by 2 if it leaves a remainder of 1, then it is an odd number.
The difference between any two successive/consecutive odd numbers is 2.

Product  rule:
odd x odd = odd: 3 x 5=15
odd x odd x odd = odd; 3 x 5 x 7=105
odd x odd x odd x odd=odd; 3 x 5 x 7 x 9=945
NOTE: product of n odd numbers is always odd.

Sum rule:
odd + odd = even ;  1 + 3 =4
odd + odd  + odd =  odd ; 1+ 3+5=9
odd + odd + odd + odd = even; 1+3+5+7=16
odd + odd + odd +odd + odd =odd: 1+3+5+7+9=25

Sum of even number of odd numbers (which is indicated in blue in the above) is always even
Sum of odd number of odd numbers (which is indicated in black in the above) is always odd.
Sum of first n positive odd integers is n²;

odd power any positive integer is always odd: odd^{(positive integer)}=odd 
  5³=125, 1¹⁰=1

odd + even = odd
odd-even =odd
odd x even= even