# Number System - Questions & DiscussionsQuantitative Report

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find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13
• @janvats  Is it 38 to the power 16!x1777 or 38 to the power of (16! to the power 1777)
In the first case  i m getting an answer of 4
16!x1777/16 gives a remainder of 1 hence the expression becomes 38^(16k+1)/17 which reduces to 38/17 by fermat's theorem which gives a remainder of 4
In the second case
16!^1777 divided by 16 gives rem of 0 hence expression becomes 38^16k which gives a remainder of 1
@td_bouncer
• consider 2nd case...dats correct way !!!
• should be 1. e(17)=16
• 1 ?
E(17) = 16
38^16k mod 17 = 1
16! mod 16k = 0
38^0)^1777 mod 17 = 1^1777 mod 17 = 1
• (34+4)^16!*1777/17
4^16!*1777/17
16^16!*1777/17
(17-1)^16!*1777/17
(-1)^16!*1777/17
(1)^1777/17
1,Ans
• option a
• I think ans is 1 As we solve step by step 1777 divide by17 so eulr coeffient =16 gives 1 now now whole change into 38^16! /17 so euler coeffient 16 so remainder 1