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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.
What else can I help you with?
Is the sum of any two consecutive integers always odd?
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.
The sum of three consecutive odd intrgers is 228 what are the inetgers?
This has no answer. The sum of three odd integers is always odd.
What are two consecutive integers for 52?
They are consecutive odd integers: 25 and 27.
The sum of two consecutive odd integers?
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.
What is the sum of 3 consecutive odd integers that is at least 162 the minimum sum?
3 odd integers must total an odd number. 3 consecutive odd integers must total a multiple of 3. The lowest number greater than 162 which satisfies these requirements is 165, ie 53 + 55 + 57
The sum of three consecutive even integers is -7Find the 3 integers?
There is no solution. The sum of multiple even integers will always be even, and -7 is odd.
What are consecutive integers with the sum of 116?
The sum of two consecutive integers will always be an odd number.
Is the sum of any two consecutive integers always odd?
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.
What are the consecutive odd integers of 152?
find the two consecutive odd integers with a sum of 152
The sum of three consecutive odd intrgers is 228 what are the inetgers?
This has no answer. The sum of three odd integers is always odd.
What are two consecutive numbers that add up to 600?
The sum of consecutive integers will always be odd. Consecutive odd numbers will be even. 299 + 301 = 600
Why 35 and 7 are the only three consecutive odd prime numbers?
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.
Find two consecutive odd integers whose sum is 195?
That's not possible. Adding two odd integers, the result will always be even.
What are two consecutive integers for 52?
They are consecutive odd integers: 25 and 27.
The sum of two consecutive odd integers?
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.
Why can you not find 2 consecutive odd numbers that have a sum of 29?
29 cannot be the sum of two odd integers. The sum of two odd integers is always an even integer.
What is the sum of 3 consecutive odd integers that is at least 162 the minimum sum?
3 odd integers must total an odd number. 3 consecutive odd integers must total a multiple of 3. The lowest number greater than 162 which satisfies these requirements is 165, ie 53 + 55 + 57
