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Are all perfect square number are even numbers?
No, all perfect square numbers are not even numbers. Eg. the square of 3 is 9. (32=9) To generalize the proof: If p is odd then p=2n+1 and p2=(2n+1)2=4n2+4n+1=2(2n2+2n)+1 So odd numbers have odd square
What is an odd number multiplied by an odd number?
A definition of an odd number is 2n-1 where n is any integer. The product of two odd numbers is thus (2n-1)(2p-1) for any numbers n and p. Expanding the expression yields 2(2pn -(p+n)) + 1. The term on the left is even by definition. Adding 1 to any even number is, by definition, an odd number. Therefore, the conclusion is elementary (Watson); the product of two two odd numbers is an odd number
Is p2 plus p an odd or even number?
Even
When you multiply an odd number and an even number is your answer always odd?
No, it's always even, and here's the proof: All even numbers can be expressed as 2n, where n is any integer. All odd numbers can be expressed as 2p + 1, where p is any integer. Multiply those two together: 2n(2p + 1) = 2(2np + n). Since both 2np and n are integers, that means 2np + n is an integer; and since that integer is being multiplied by 2, it must be even.
Why do two even numbers always equal an even number?
On a number line, adding an even number to another number (or zero) results in an even displacement, which must end in the same type of number as the original. If the beginning number is odd, adding an even number produces an odd sum. If the beginning number is even, adding an even number produces an even number. A corollary is that: Adding two like numbers produces an even number. Adding two unlike numbers produces an odd number. ---------------------------------- Algebraically: let x be an even number, Then y = 2x for some value of x Two even numbers would be 2m and 2n Adding them gives: 2m + 2n = 2(m + n) = 2p where p = m + n; 2p is of the form y = 2x, so 2p is an even number. Thus adding two even numbers results in an even number. Similarly for odd numbers: If y = 2x is an even number then z = y + 1 = 2x +1 is an odd number. Two odd numbers would be 2m+1 and 2n+1 Adding them gives: 2m+1 + 2n + 1 = 2m + 2n + 2 = 2(m + n + 1) = 2p where p = m + n + 1 Thus adding two odd numbers results in an even number. Similarly for one even and one odd number. An even number would be 2m and an odd number would be 2n+1 Adding them gives: 2m + 2n + 1 = 2(m + n) + 1 = 2p + 1 where p = m + n Thus adding an even number and an odd number results in an odd number.
