What is remainder
((4^17)+(17^4))/7 ??

• 1st let us consider 4^17/7
  i.e ((4^3)^5 x 4^2)/7
  4^3/7= 1(remainder) therefore now (1^5 x 4^2)/7 = (1 x 16)/7 = 2(remainder)
  
  now consider (17^4)/7
  i.e 17/7 = 3(remainder) therefore
  (3^4)/7 = 81/7= 4(Remainder)
  
  therefore total 2+4=6 rem(Ans)
  
• 10 years agoHelpfull: Yes(31) No(6)
• 4^17=unit digit 4,
  17^4 unit digit=1
  so 1+4=5
  5/7 gives 5 as remainder
  ans=5
  
  
• 10 years agoHelpfull: Yes(9) No(4)
• 4^17=unit digit 4,
  17^4 unit digit=7
  so 7+4=11
  11/7 gives 4 as remainder
  ans=4
• 10 years agoHelpfull: Yes(6) No(12)
• 4^17 mod 7= (7-3)^17 mod 7= (-3)^17 mod 7 {since, 7^17 mod 7=0}
  but -3^3 mod 7= -27 mod 7= 1 => -3^17= (-3^3)^5 mod 7 x -3^2 mod 7= 1x5= 5
  also
  17^4 mod 7= (7*2+3)^4 mod 7= 3^4 mod 7 {{since, (2*7)^4 mod 7=0}}
  =81 mod 7= 4
  Hence (5+4) mod 7= 2 (Ans)
• 10 years agoHelpfull: Yes(5) No(3)
• ans is 0.
  
• 10 years agoHelpfull: Yes(3) No(7)
• 5
  
  4^17+17^4
  REM 4+ REM 1
  5/7
  =5
• 10 years agoHelpfull: Yes(1) No(1)
• (4^17+17^4)/7
  =(2^34+(14+3)^4)/7
  =((2^3)^31)/7+((14+3)^4)/7
  =(8^31)/7+(3^4)/7 [as 14 or its multiples are always divisible by 7]
  =((7+1)^31)/7+(27/7)+(3/7)
  =1/7 (remainder) + (28-1)/7 + 3/7
  =1/7 +(-1/7) (remainder) +3/7
  =3/7
  
  so the remainder is 3
• 10 years agoHelpfull: Yes(1) No(2)
• ((4^3)^5 .4^2)/7
  since 64/7 gives 1
  thus 1*4^2/7=16/7 gives 2 as remainder .........1
  
  17/4 gives 3 as rem
  so 3*3*3*3/7 gives 1 remainder from (27/7) and 3 from 3/7 so 3 as the remainder ......2
  from 1 and 2 we have 6 as the remainder
• 10 years agoHelpfull: Yes(0) No(0)
• because (2^10)^odd=24 than from question 4^17= 2^17+2 =2^19 =24
  and 17^4=83521 now add both number 24+83521=83545 divide by 7 which is equal to 11935 and remainder should be 0.
• 10 years agoHelpfull: Yes(0) No(1)
• 4 power odd num is 4...7 power 4 is 1(unit digit)...4+1=5...5/7...remainder is 2
• 10 years agoHelpfull: Yes(0) No(0)