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.
No, the sum of any two consecutive integers is always even. For example, if we take two consecutive integers ( n ) and ( n+1 ), their sum is ( n + (n + 1) = 2n + 1 ), which is an odd number. However, if we consider the sum of integers with an even and an odd integer, the result is always odd. Thus, the statement is not accurate as framed.
This has no answer. The sum of three odd integers is always odd.
They are consecutive odd integers: 25 and 27.
Are not all integers spaced out to be odd then even then odd then even etc (eg 1,2,3,4,5,6,7,8,9,10, etc) and therefore there is no such thing as two consecutive odd integers.
For any integer n, the numbers 2n + 1 and 2n + 3 are consecutive odd integers.
There is no solution. The sum of multiple even integers will always be even, and -7 is odd.
The sum of two consecutive integers will always be an odd number.
find the two consecutive odd integers with a sum of 152
This has no answer. The sum of three odd integers is always odd.
If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.
The sum of consecutive integers will always be odd. Consecutive odd numbers will be even. 299 + 301 = 600
That's not possible. Adding two odd integers, the result will always be even.
They are consecutive odd integers: 25 and 27.
29 cannot be the sum of two odd integers. The sum of two odd integers is always an even integer.
Are not all integers spaced out to be odd then even then odd then even etc (eg 1,2,3,4,5,6,7,8,9,10, etc) and therefore there is no such thing as two consecutive odd integers.
It will alway be even, because it will always be the product of an odd and an even number, which is always even.
For any integer n, the numbers 2n + 1 and 2n + 3 are consecutive odd integers.