4meonly wrote:If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?

A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

OA Soon

Only way 2066^z can be the divisor of 3176793, when z = 0

Because they both are not divisible by any integer from 2-7

then 2066^0 = 1, and 1 is the divisor of every number

x could be any integer

z^x - x^z = 0^x - x^0 = 0 - 1 = -1

Hence, B

OA?

Yup agree with PC on B

Z is a non negative integer , you can take this as a clue that you have to consider 0 as well.

Plus 2066^n the units digit will always be 6 and there is no integer which when you multiply by 6 you'll get a units digit of 3.

So z is 0.

0-1 = -1.

Yes, folks, u r correct.
OA B

The key here is to understand that z=0.

4meonly wrote:If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?

A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

OA Soon

Since gcd(3,176,793)=1 =>z=0 =>z^x - x^z=-1

If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?

A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined



3176793 is a ODD number
so we don't expect any even no as its factor

2066 is a even number

hence 2066 or its multiple cannot be divisior.

So z = 0

hence IMO B