Proof of the fact that if a|b and a|c, then a|(b+c)
2.3
Suppose that a|b and a|c.
By the definition of divisibility, a|b means that there is an integer s
such that
b = as.
Similarly, there is an integer t such that
c = at.
Hence, b+c = as+at = a(s+t).
Therefore, a|(b+c).
End of proof.
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