Remainder of 2^47/47 ?

plz explain completely how to solve this kind if questions

• first check whether the divisor is a prime number. in this question it is.
  therefore according to theorem, if the power of the dividend is equal to the number of co-primes below the divisor then its remainder will be 1.
  
  1) 47 is prime
  2)coprimes below 47 are 46 as all the numbers below a prime number are coprime to it.
  
  therefore we r interested to convert power of 2^47 to 2^46 as then according to the theorem remainder will be 1.
  
  implies, 2^47/47=2x(2^46)/47 = 2x(1)=2
• 9 years agoHelpfull: Yes(12) No(1)
• instead of going for the full solution just remember
  (2^prime no.)/prime no. will give remainder 2
  where (prime no. != 2) for denominator..
• 9 years agoHelpfull: Yes(4) No(1)
• (2^10*2^10*2^10*2^10*2^7)/47
  (1024*1024*1024*1024*128)/47
  (37*37*37*37*34)/47
  (1369*1369*34)/47
  (6*6*34)/47
  (6*16)/47
  =2
• 9 years agoHelpfull: Yes(2) No(0)
• (a^p/p)=a...Fermat little theorem
  So ans=2
  (a^(p-1))/p=1
  So ans=2
• 9 years agoHelpfull: Yes(2) No(0)
• Eular number of 47 is 47 i.e E(47)=47
  2^47/47= [2^(47/E(47))]/47=(2^0)/47=2
  so reminder 2
  
• 9 years agoHelpfull: Yes(0) No(0)
• ans is 8. because 47/4 remainder is 3 so 2^3=8 and 8/47 so remainder is 8
• 9 years agoHelpfull: Yes(0) No(9)
• ans is 2.
  lets take 2^3/3 rem is 2
  and in same way 2^5/5=2.........................2^47/47=2
• 9 years agoHelpfull: Yes(0) No(0)
• 2^47/47 = 2*2^46/47
  =2*1/47
  =rem 2
• 9 years agoHelpfull: Yes(0) No(0)
• Ans 1 break if by 64*64*64*64*64*64*64*32/47
• 9 years agoHelpfull: Yes(0) No(1)