For the problem above, no I cannot think of two numbers whose sum is an odd number.
Consider these statements:
If 3+5=8 5+7+11 = 23 9+13+21=43
a) If a,b,c are three odd numbers then a+b+c is an odd number as well.
b) An odd number is represented by 2m+1 with m∈Z
So we let:
a = 2x+1
b = 2y+1
c = 2z + 1
with x,y,z∈Z
To show that the statement above about the sum of two number being even:
a + b = (2x+1) + (2y+1) = 2x+2y+2 = 2(x+y+1)
Therefore it is TRUE
but is it true that 3 odd numbers have a sum that is odd?
a + b + c = (2x+1) + (2y+1) + (2z+1) = 2x + 2y + 2z + 3= = 2(x+y+z+1) + 1
We let x+y+z+1=m, since x,y,z are integers then m is an integer as well:
a+b+c = 2m + 1
This has the same form as above
Therefore the sum of three odd numbers is odd
