Answer:
I will answer it in English:
a) We have te number N = 4752a
if we want to divide it by 3, then the addition of all the digits must be a multiple of 3.
Sum = 4 + 7 + 5 + 2 + a = 6 + 7 + 5 + a = 18 + a
and 18 is a multiple of 3, then we can have, a = 0, a = 3, a = 6, a= 9
b) A number is divisible by 5 if it ends on 5 or 0, so the possible values of a are 0 and 5.
c) we know that 15*3 = 45
then 15*3000= 45000
now we have:
4752a - 45000 = 252a
15*13 = 2520
then we have that a must be equal to zero, and:
15*(13 + 3000) = 47520
d) We want a number that when we divide it by 7, the surpass is 5.
a number is divisible by 7 if the difference between the number without the units and the double of the units is 0 or a multiple of 7.
in N = 4752x the unit is a, then we have:
D = 4752 - 2*x
now, let's choose a such we have a multiple of 7
we know that 5746 is a multiple of 7, so we can choose x= 3 and get:
D = 4752 - 2*3 = 5746
So the number N = 47523 is a multiple of 7, and when we divide it by 7 we will have a surpass of 0.
Then when we divide N + 5 by 7, we will have a surpass of 7.
This is: N + 5 = 47528
This means that the actual value of a that we need is 8.
