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Homework Statement
Evaluate (16^1000 - 18^2000)(mod 17)
Homework Equations
I'm not sure how to go about doing this, but I realise it has something to do with the pattern from the last digit obtained from the 2 large numbers
That's really not a great realization. I would think about what 16 and 18 are mod 17.Homework Statement
Evaluate (16^1000 - 18^2000)(mod 17)
Homework Equations
I'm not sure how to go about doing this, but I realise it has something to do with the pattern from the last digit obtained from the 2 large numbers
The Attempt at a Solution
What's (-1)^1000-1^2000? (x mod 17)^n mod 17=(x^n) mod 17. Right?16(mod 17) = -1 and 18(mod 17) = 1, how do I go from here?
16 and (-1) are congruent mod 17 since they differ by 17. So (-1)^1000=16^1000 mod 17. You can use either form in your calculation. Which one makes it easy?Turns out 16(mod17) is 16, so how would I go about calculating 16^1000 seeing that the exam does not permit calculators? So would the solution be 16^1000 - 1^2000? So is the solution 15? Because using the calculator returns 0 which I don't think is right