
(Continued )
A: Let n be an integer number with n = ±a
4
a
3
a
2
a
1
a
0
,0≤ a
i
≤ 9 for all i =0,1,2,3,4,anda
4
≠ 0, such
that a
4
+ a
3
+ a
2
+ a
1
+ a
0
=3t,wheret is an integer number. (The fact tha t n is an integer number is
an implicit hypothesis, since the concept of divisibility is defined only for integer numbers. The ± sign
indicates that the number n can be either positive or negative.)
B: The number n is divisible by 3; that is, n =3s with s an integer number.
Proof: As the hypothesis provides information about the digits of the number, we will separate the digits using
powers of 10. For sake of simplicity, let us assume that n is positive. Thus,
n = a
4
a
3
a
2
a