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Is an odd number times an odd number always an odd answer?
Yes, it is.
The product of odd numbers is always even?
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. Odd times odd is always odd.
Why is the product of two odd numbers odd?
Let me show this to you by an example : Suppose we wish to multiply 3 and 7. Product or Multiplication by any device is actually carried by the process of addition of 3 seven times, i.e. 3+3+3+3+3+3+3 = 21. Because the two numbers are odd, the result is always odd. To Summarize, addition of an odd number(i.e. 3) to itself an odd number of times(i.e. 7) always results in an odd number. The product of an even and an odd number always results in an even number because addition of even number any number of times is always even and an odd number added to itself an even number of times also results in an even number. For ex. 7*2 = 14, here 7(odd number) is added 2(even number) times, i.e. 7+7=14 which is even.
Does an odd number minus an odd number have an odd answer?
No, it always has an EVEN answer
Is the sum of two square consecutive numbers an odd number?
Yes. One has to be the square of an odd number. The other square has to the the square of the even number either before or after the odd number. If this is confusing just plug in real values. In either case, an odd times and odd is odd. Therefore one of the squares has to be odd. AN even times an even, however, is always even. Therefore, the second square has to be even. Thus, one of the squares is even and the other is odd. An even plus and odd is always odd.
