Almightytay1931 Almightytay1931
  • 14-09-2019
  • Mathematics
contestada

If aſc and a +b = C, prove that a|b.

Respuesta :

Nehuen
Nehuen Nehuen
  • 18-09-2019

Answer:

Assuming a being a divisor of c and [tex]a,b,c \in \mathbb{Z}[/tex]

Step-by-step explanation:

We are told that [tex]a \mid c[/tex]

and that [tex]a+b =c[/tex]

which means that

[tex]\exists k \in \mathbb{N}[/tex] so that [tex]c = k.a[/tex]

so we can rewrite [tex]a+b[/tex] as

[tex]a+b = c = k.a[/tex]

[tex]b = k.a-a = (k-1).a[/tex]

and as [tex]k \in \mathbb{N}[/tex]

We have that either

Showing that [tex]a \mid c[/tex]

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