f(x)=1+x+x^2+x^3+....+x^6
find reminder when f(x^7)devided by f(x)

• ans is 7
  1+x+x^2+.....+x^6=(x^7-1)/(x-1)
  x^7-1=x-1(1+x+x2...x7)
  f(x^7)=1%f(x)+(x^7)^1%f(x)+(x^7)^2......+(x^7)^6
  f(x7)=1+(x^7-1+1)%f(x)+(x^7-1+1)(x^7-1+1)%f(X)........
  f(x7)=1+(x^7-1)%f(x)+1%f(x)+(((x^7-1)%f(x)+1/f(X))(x^7-1)+1/f(X))..
  f(x^7)%f(X)=1+1+1+1+1+1+1=7
• 10 years agoHelpfull: Yes(6) No(16)
• if we take x value as 1 then f(1)=7
  f(1^7)=7 why because 1 power any number is always 1
  then f(x^7)/f(x)=1
  so that remainder is 0
  
• 10 years agoHelpfull: Yes(4) No(0)
• f(x^7) gives 6 term in f(x),so it divided by f(x^7) means remainder value zero
  
• 10 years agoHelpfull: Yes(0) No(0)