GATE CS 2016 Set 2 — Question 39
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Engineering Mathematics → Sets & Combinatorics → Groups, Rings & Fields
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Question
The value of the expression , in the range 0 to 16, is ________.
Correct answer
4 to 4
Solution
To find the value of :
To bring into the range 0 to 16:
Thus, the value of in the range 0 to 16 is 4.
1.Identify the modulus: The modulus is 17, which is a prime number.
2.Apply Fermat's Little Theorem: Since 17 is prime and 13 is not divisible by 17, we have:
3.Reduce the exponent: We divide the exponent 99 by 16 to find the remainder:
So, .4.Simplify the expression:
Substituting the result from Fermat's Little Theorem:5.Calculate :
To bring into the range 0 to 16:
Thus, the value of in the range 0 to 16 is 4.
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