2007-07-02 10:30:22 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Easy. 5 = 1 mod 4 Plug in the 1: 1^n +3 = 4 . Therefore,
4 divides 5^n +3 for all nonnegative integers.
2007-07-02 11:23:15 · answer #1 · answered by knashha 5 · 1⤊ 1⤋
You can prove it by induction.
5^0 + 3 = 4, divisible by 4.
Assume 5^n + 3 is divisible by 4.
Then 5(5^n + 3) is also divisible by 4.
5(5^n + 3) = 5^(n+1) + 15
= 5^(n+1) + 3 + 12
Since the whole thing is divisible by 4 and 12 is divisible by 4, it must be that 5^(n+1) + 3 is also divisible by 4.
So 5^n + 3 is divisible by 4 for all natural n.
2007-07-02 17:47:29 · answer #2 · answered by TheSpoon 2 · 0⤊ 0⤋
It can be. 5^3+3=128 and 128/4=32; 5^2+3=28 and 28/4=7, for example; 5^4+3=628 and 628/4=157. Can you prove that it is divisible by 4 for all values of n?
2007-07-02 17:38:21 · answer #3 · answered by skipper 7 · 0⤊ 0⤋
5^n=1^n=1 mod 4
5^n+3=1+3 =4=0 mod 4
So
5^n+3 is divisible by 4
2007-07-03 17:49:15 · answer #4 · answered by zohair 2 · 0⤊ 0⤋
5^n + 3
if n = 1. . . . . 5 + 3 = 8 . . . . is divisible by 4
if n = 2. . . . . 25 + 3 = 28 . . . . is divisible by 4
if n = 3. . . . . 75 + 3 = 78 . . . . is not divisible by 4
if n = 4. . . . . 625 + 3 = 628 . . . . is divisible by 4
if n = 5. . . . . 3125 + 3 = 3128 . . . . is divisible by 4
if n = 6. . . . . 15625 + 3 = 15628 . . . . is NOT divisible by 4
answer: not divisible by 4
2007-07-02 17:40:49 · answer #5 · answered by CPUcate 6 · 0⤊ 0⤋
yes it is. CPU, when n = 6, it is divisible by 4.
2007-07-02 17:57:52 · answer #6 · answered by swd 6 · 0⤊ 0⤋
Yes , for all n>= 0
2007-07-02 17:35:21 · answer #7 · answered by ironduke8159 7 · 0⤊ 0⤋
n its not divisble by it.
2007-07-06 07:07:51 · answer #8 · answered by ♫●GARV●♫ 6 · 0⤊ 0⤋