find the remainder when 15^2010+16^2011 is divided by 7 ??

• (15^2010+16^2011)/7
  15^2010/7=(2*7+1)^2010/7=1^2010/7, rem=1
  16^2011/7=(2*7+2)^2011/7=2^2011/7=(2^3)^670*2/7=(7+1)^670*2/7=1^670*2/7=2/7, rem=2
  so 15^2010+16^2011/7 gives remainder=(1+2)/7=3/7
  remainder=3
• 10 years agoHelpfull: Yes(32) No(6)
• remainder=3
• 10 years agoHelpfull: Yes(12) No(3)
• (15^2010+16^2011)/7
  15^2010/7=(2*7+1)^2010/7=1^2010/7, rem=1
  16^2011/7=(2*7+2)^2011/7=2^2011/7=(2^3)^670*3/7=(7+1)^670*3/7=1^670*3/7=3/7, rem=3
  so 15^2010+16^2011/7 gives remainder=(1+3)/7=4/7
  ans remainder=4
  this one is correct.
• 10 years agoHelpfull: Yes(10) No(24)
• Here is Correct Answer:
  Que. -(15^2010+16^2011)/7
  =(15^2*1005)/7+((16^3)^670)*16/7
  now 15^2/7 leaves remainder 1 and 16^3/7 also leaves a remainder of 1.
  so that,
  =1+(1*16/7)
  As 16/7 leaves a remainder of 2.
  =1+2
  Therefore Remainder of the expression is equal to 3.
• 10 years agoHelpfull: Yes(9) No(1)
• (15^2010+16^2011)/7
  15^2010/7=(2*7+1)^2010/7=1^2010/7, rem=1
  16^2011/7=(2*7+2)^2011/7=2^2011/7=(2^3)^670*2/7=(8-1)^670/7=(-1)^670*2/7=2/7, rem=2
  so 15^2010+16^2011/7 gives remainder=(1+2)/7=3/7
  ans remainder=3
• 10 years agoHelpfull: Yes(3) No(1)
• remainder is 2
  
• 10 years agoHelpfull: Yes(2) No(1)
• 4 rem
  by doing
• 10 years agoHelpfull: Yes(2) No(2)
• 15^2012 is 11
  16^2011 is 6
  11+6=17
  17/7 remainder is 3
• 10 years agoHelpfull: Yes(2) No(1)
• (15^2010+16^2011)/7
  15^2010/7=(2*7+1)^2010/7=1^2010/7, rem=1
  16^2011/7=(2*7+2)^2011/7=2^2011/7=(2^3)^670*3/7=(8-1)^670/7=(-1)^670*3/7=3/7, rem=3
  so 15^2010+16^2011/7 gives remainder=(1+3)/7=4/7
  ans remainder=4
• 10 years agoHelpfull: Yes(1) No(16)
• 15/7 remainder = 1 and 1^2010=1
  16/7 remainder = 2 and 2^2011= ((2*2*2)^670 * 3)/7= 3
  so remainder = 1+3 =4
• 10 years agoHelpfull: Yes(1) No(9)
• 5 power anything is 5 6 power anything is 6 (5+6)=11/7=4
  
• 9 years agoHelpfull: Yes(1) No(0)
• I think this is correct 15^2010+16^2011 can be written as (1+5)^(2+0+1+0)+(1+6)^(2+0+1+1)= 6^3+7^4=2162401=2617. now by dividing 2617 with 7 we get remainder as 6. therefore answer is 6.
• 10 years agoHelpfull: Yes(0) No(4)
• I think this is correct 15^2010+16^2011 can be written as (1+5)^(2+0+1+0)+(1+6)^(2+0+1+1)= 6^3+7^4=216+2401=2617. now by dividing 2617 with 7 we get remainder as 6. therefore answer is 6.
• 10 years agoHelpfull: Yes(0) No(5)
• 15 divided by 7 leaves 1 remainder and it leaves 1 also for 15^2010 similarly for 16^2011 it leaves 2 and the sum leaves 1+2 that is three(3) as the remainder
• 10 years agoHelpfull: Yes(0) No(0)
• since remainder always depend on unit digit
  so unit didits are (15^2010)=5 and (16^2011)=6
  by diving we get remainders as 3 and (-1) respectively so remainder is 3+(-1)=2
• 10 years agoHelpfull: Yes(0) No(1)
• remainder=3
  
• 10 years agoHelpfull: Yes(0) No(0)
• (15^2010+16^2011)/7
  15^2010/7=(2*7+1)^2010/7=1^2010/7, rem=1
  16^2011/7=(2*7+2)^2011/7=2^2011/7=(2^3)^670*2/7=(7+1)^670/7=(1)^670*2/7=2/7, rem=2
  so 15^2010+16^2011/7 gives remainder=(1+2)/7=3/7
  ans remainder=3
• 10 years agoHelpfull: Yes(0) No(1)
• 1+2=3.3Is remainder
  
• 10 years agoHelpfull: Yes(0) No(0)
• (15+16)/7= 31/7 = 3
  
• 10 years agoHelpfull: Yes(0) No(0)