lazyashell wrote:
If p is an odd prime number, and if 5 is a factor of \(p + p^2\), which of the following might be the remainder when p is divided by 5?
Indicate all such numbers.
A.0
B.1
C.2
D.3
E.4
We can factor the given expression as follows: \(p + p^2 = p(p+1)\)
So the given information is telling us that 5 is a factor of \(p(p+1)\)
This means 5 could be a factor of p, or 5 could be a factor of p+1
Let's examine each possible case:
case i: 5 is a factor of p
Another way to say this is:
p is a multiple of 5If p is a multiple of 5, then we will get a remainder of
0 when we divide p by 5
case ii: 5 is a factor of p+1
Another way to say this is:
p+1 is a multiple of 5 So, some possible values of p+1 are: 5, 10, 15, 20, ....
If p + 1 = 5, then p = 4. When we divide 4 by 5, the remainder is
4If p + 1 = 10, then p = 9. When we divide 9 by 5, the remainder is
4If p + 1 = 15, then p = 14. When we divide 14 by 5, the remainder is
4Answer: A, E