what is the reminder when 6^17+17^6 is divided by 7 ?
a) 3 b) 0 c) 6 d) 1

• ((7-1)^17+(14+3)^6)/7 --> ((-1)^17+(3)^6)/7 --> ((-1)+remainder(1))/7 --> (remainder(6)+remainder(1))/7 --> 7/7=0
• 12 years agoHelpfull: Yes(22) No(8)
• unit digit of 6^17=6...
  6^1=6
  6^2=6
  6^3=6
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  6^17=6
  unit digit means calculate only last digit
  therefore 6^17 reminder=6 why means (6/7)
  same other part reminder=2 why means 9/7=2
  reminder(6)+reminder(2)/7=1(8/7=1)
  show the answer=1
• 12 years agoHelpfull: Yes(7) No(5)
• ans : d)1
  consider only unit digits....
• 12 years agoHelpfull: Yes(6) No(7)
• 6^2=1 mod 7 [(6^2)=36,divided by 7 gives remainder 1]
  =>(6)^2*8=1^8 mod 7
  =>6^16=1 mod 7 [all even power also gives 1 mod 7]
  =>(6^16)*6=1*6 mod 7
  So, 6^17=6 mod 7.
  
  Likewise,
  
  17^2=2 mod 7
  =>(17)^2*3=2^3 mod 7
  =>17^6=8 mod 7 [simplify: 8 is one time divisible by 7 & gives remainder 1]
  So, 17^6=1 mod 7.
  
  ((6^17+17^6)/7)= ((6 mod 7)+(1 mod 7))/7
  =>((6+1) mod 7)/7
  =>(7 mod 7)/7
  =>Hence the remainder is 0
• 12 years agoHelpfull: Yes(4) No(0)
• 6^17 mod 7=(7-1)^17 mod 7=(-1)^17 mod 7=-1
  17^6 mod 7=(7*2+3)^6 mod 7= (3)^6 mod 7=729 mod 7=1
  the remainder when 6^17+17^6 is divided by 7 is
  1-1=0(ans)
• 12 years agoHelpfull: Yes(2) No(0)
• find unit place by divide power by 4 if remainder comer becomes power of unit place so
  6^1+7^2=55
  55/7=remainder=3
• 12 years agoHelpfull: Yes(1) No(2)
• ans is zero
  
• 12 years agoHelpfull: Yes(1) No(0)
• 6^17 mod 7=(7-1)^17 mod 7=-1^17 mod7=-1 mod 7=(-1+7)mod 7=6mod7=6(a mod n can range only between 0 and n-1)
  (7*2+3)^6 mod 7=14^6 mod 7+ 3^6mod 7=0+729 mod 7=1
  Thus 6+1=7 is remainder but value can range between only 0 and 6 so again divide by 7 so 7 mod 7=0
  Hope this helped... -1 mod 7 is not -1
• 11 years agoHelpfull: Yes(0) No(0)