0
Still curious? Ask our experts.
Chat with our AI personalities
Vivi
Ezra
Blake
Add your answer:
Earn +20 pts
If n is an odd integer prove 8 divides n of n-1?
9
Is an odd integer greater than 40?
The next odd integer after 40 is 41
Is the sum of one odd number and one even number even or odd prove and explain in words?
The sum of an odd and an even number is odd. Any odd number can be expressed as 2n + 1 (for some integer "n"). Any even number can be expressed as 2m (for another integer, "m"). The sum of the two is 2(m+n) + 1. Since the expression in parentheses is an integer, multiplying it by 2 gives you an even number. Adding 1 makes the entire expression odd.
What kind of number is 71?
The number 71 is an integer, an odd integer, a positive odd integer, and also a prime number.
Why is the sum of consecutive odd integers always a multiple of 4?
It is quite easy to prove this using algebra. Suppose x is the smaller of the two odd integer. The fact that x is odd means that it is of the form 2m + 1 where m is an integer. [m integer => 2m is an even integer => 2m + 1 is odd] The next odd integer will be x + 2, which is (2m + 1) + 2 = 2m + 3 The sum of these two consecutive odd integers is, therefore, 2m + 1 + 2m + 3 = 4m + 4 = 4(m + 1) Since m is an integer, m+1 is an integer and so 4(m + 1) represents a factorisation of the answer which implies that 4 is a factor of the sum. In other words, the sum is a multiple of 4.
