Question
Find the remainder when 4001000 is divided by 17?
Answer: Option B
:
B
This needs the application of basic remainder, fermat theorem and frequency
Step 1 - Remainder when 400 is divided by 17 is 9
The problem changes to 9100017
From fermat theorem, the Euler's number of 17 is 16.
1000=16k +8
Problem now changes to 9817
Going by frequency method, 9417 gives remainder -1 so 9817 will give remainder 1.
Altenative solution :
We know tha 92=81=>(81)500=>(−4)500=>16250=>(−1)250=1
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:
B
This needs the application of basic remainder, fermat theorem and frequency
Step 1 - Remainder when 400 is divided by 17 is 9
The problem changes to 9100017
From fermat theorem, the Euler's number of 17 is 16.
1000=16k +8
Problem now changes to 9817
Going by frequency method, 9417 gives remainder -1 so 9817 will give remainder 1.
Altenative solution :
We know tha 92=81=>(81)500=>(−4)500=>16250=>(−1)250=1
Was this answer helpful ?
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