MHB Gre.al.13 sum of even and odd numbers

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The discussion centers on determining conditions under which the sum of two integers, m and n, is always odd. It is established that if m is odd and n is even, or vice versa, the sum will be odd. Conversely, if both integers are odd or both are even, the sum will be even. The user expresses uncertainty about the underlying theory but attempts to illustrate the concepts with examples. The consensus indicates that option e, where m is odd and n is even, is the correct condition for achieving an odd sum.
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$\tiny{gre.al.13}$
For which of the following conditions will the sum of integers m and n always be an odd integer.?
a. m is an odd integer
b. n is an odd integer
c. m and n both are odd integers
d. m and n both are even integers
e. m is an odd integer and n is an even integerI chose e just playing with numbers
don't know the exact theory on this
 
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Say m and n are even. Then we can say that m = 2p and n = 2q. So m + n = 2p + 2q = 2(p + q), which is even.

Say m is odd and n is odd. Then we can say m = 2p + 1 and n = 2q + 1. Etc.

-Dan
 
got it

never liked number theorem questions
 
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