Posted by **Sally** on Wednesday, February 15, 2012 at 7:52am.

Is 4^33 + 3^44 divisible by 5?

Please help ASAP. This is due tomorrow. Thank you very much :)

- Math -
**Reiny**, Wednesday, February 15, 2012 at 8:31am
yes

look at powers of 4

4^1 = 4

4^2 = 16

4^3 = 64

4^4 =256

....

every even indexed power ends in 6, every odd indexed power ends in 4

so 4^33 ends in 4

now look at the powers of 3

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

...

the answers end in 3 9 7 1 3 9 7 1 ...

even exponents end in either 9 or 1

if the even exponent is also a multiple of 4, the answer ends in a 1

so 3^44 will end with a 1

so if we add a number ending in 4 to a number ending in 1

we get a number ending in 5 which is divisible by 5

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