SOLUTION: Use direct proof to prove that the sum of two odd integers say a and b is even. Note that we have discussed an odd number to be represented by 2n+1 and even as 2n.

Algebra ->  Linear-equations -> SOLUTION: Use direct proof to prove that the sum of two odd integers say a and b is even. Note that we have discussed an odd number to be represented by 2n+1 and even as 2n.      Log On


   

Question 1189131: Use direct proof to prove that the sum of two odd integers say a and b is even. Note
that we have discussed an odd number to be represented by 2n+1 and even as 2n.
Answer by ikleyn(52784) About Me  (Show Source):
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Use direct proof to prove that the sum of two odd integers say a and b is even. Note
that we have discussed an odd number to be represented by 2n+1 and even as 2n.
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Let "a" and "b" be odd integer numbers.


Then, as you discussed earlier,  a = 2n+1, b = 2m+1  for some integer numbers "m" and "n".


It implies that  a + b = (2n+1) + (2m+1) = 2n + 1 + 2m + 1 = 2n + 2m + 2 = 2*(n+m+1).


Thus the sum a + b is an integer number of the form 2k, where integer number "k" is n+m+1.


It means that  a + b  is an even number.

The proof is complete.