Question

Compute the units digit of 17^2012+11^2012-7^2012

Answer 1

Answer:

The units digit is 1.

Step-by-step explanation:

To identify the last digit or the unuts digit of a number, we use the concept of cyclicity. Numbers last digit has their own specific cycle.

The cycle for number 17,

17 - 7 (units digit)

17x17 - 9 (units digit)

17x17x17 - 3 (units digit)

17x17x17x17 - 1 (units digit)

For number 11, all units digit is 1.

For number 7, it follows the same cycle of number 17.

So 17 and 7 has 4 elements in the cycle (7, 9, 3 1) and only (1) for 11.

Divide 2012 by 4, we get 503. This means that we have 503 times the cycle of 4 is repeated. The fourth element in the cycle is 1. Thus 17^2012 has 1 as units digit,

11^2012 has 1 as units digit

And 7^2012 has 1 as units digit.

So 1+1-1 =1.