Question:-
Determine the remainder when 72018 is divided by 2017.


Please provide the applicable and reasonable solution in steps.
{Please don't provide certified answer... I want only experts answer to any without providing any weblink or certifiied answer} 

 

Hi, We know that ap-1p leaves remainder 1  meaning number of the form ap-1 when divided by p  leaves remainder 1, where p is a prime number and a,p are co-prime So here p = 2017 is a prime number and a,p or 7,2017 are co prime But in our question power of 7 is 2018 not p-1 or 2016 so lets get it in the form of 2016 so 720182017=72016+22017=72016×722017=720162017×49= 72017-12017×49so here remainder of 72017-12017 is 1 and it will be multiplied by 49 so over all remainder is 49. 

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