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Mathematics
Jewel Logan
27 February, 21:21
Compute the units digit of 17^2012+11^2012-7^2012
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Kamryn Bridges
27 February, 21:38
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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.
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