What is the remainder when 30^100 is divided by 17?
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Answer:
Quant Primer Remainder Theorem and related concepts for CAT Preparation - Ravi Handa
handakafunda Mar 4, 2017, 11:25 AM
Are you struggling with Remainders?
Here is a bunch of questions with detail solutions.
Fermat's Theorem : Rem [a^(p-1)/p] = 1, where p is a prime number and HCF(a, p) = 1
What is the remainder of 57^67^77/17 ?
Rem [57^67^77/ 17] = Rem [6^67^77/17]
Now, by Fermat's theorem, we know Rem [6^16/17] = 1
The number given to us is 6^67^77
Let us find out Rem[Power / Cyclicity] to find out if it 6^(16k+1) or 6^(16k+2).
We can just look at it and say that it is not 6^16k
Rem [67^77/16] = Rem [3^77/16]
= Rem[(3^76*3^1)/16]
= Rem[((81^19) * 3)/16]
= Rem [1 * 3/16]
= 3
=> The number is of the format 6^(16k + 3)
=> Rem [6^67^77 /17]
= Rem [6^(16k + 3)/17]
= Rem [6^3/17]
= Rem [216/17] = 12