Harumatsu6939 Harumatsu6939
  • 17-10-2019
  • Mathematics
contestada

Prove if a and b are integers, prove that if a is even and b is even then a+b is even

Respuesta :

steffaniasierrag
steffaniasierrag steffaniasierrag
  • 18-10-2019

Answer:

Let a and b integers and suppose that are even numbers. Then, exist integers k and m such that [tex]a=2k[/tex] and [tex]b=2m[/tex].

Then,

[tex]a+b=2k+2m=2(k+m)=2n[/tex]

Since, k and m are integers then n=k+m is an integer. Then, since a + b is of the form 2 by an integer n, then a + b is an even number.

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