Question
Find the remainder when 3001000 is divided by 19?___
Answer: Option A
:
This needs the application of basic remainder theorem, Euler's theorem and frequency method.
First find the remainder when 300 is divided by 19 = 15.
The problem now changes to 15100019.
From Euler's theorem, the Euler's number of 19 is 18 (for all prime numbers, Euler's number=N-1).
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:
This needs the application of basic remainder theorem, Euler's theorem and frequency method.
First find the remainder when 300 is divided by 19 = 15.
The problem now changes to 15100019.
From Euler's theorem, the Euler's number of 19 is 18 (for all prime numbers, Euler's number=N-1).
1000=18×55+10
Problem now changes to 151019.
1519 gives remainder -4. So the remainder of (−4)1015 or (4)1015 needs to be found.
Now (4)215 gives a remainder of 1.
Going by the frequency method,
(4)1015 will give a remainder of (1)515, i.e 1.
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