20^2004+16^2004-3^2004-1 is divisible by

• (x^n-y^n) is divisible by (x-y) for all values of n
  (x^n-y^n) is divisible by (x+y) for all even values of n
  
  20^2004+16^2004-3^2004-1
  (20^2004-3^2004)+(16^2004-1^2004)
  (20^2004-3^2004) is divisible by 20-3=17 for all n
  (16^2004-1^2004) is divisible by 16+1=17 for even values of n
  (20^2004-1^2004) is divisible by 20-1=19 for all n
  (16^2004-3^2004) is divisible by 16+3=19 for even values of n
  hence (20^2004+16^2004-3^2004-1) is divisible by 17*19=323
  ANS 323
• 11 years agoHelpfull: Yes(38) No(2)
• 2 as (even+even)-(odd+odd)=even-even=even so no is divisible by 2
• 11 years agoHelpfull: Yes(15) No(1)
• 20+16-3=33
  
• 11 years agoHelpfull: Yes(1) No(2)
• (20^2004+3^2004) divisible by (20-3)=17 {by rule (a^n-b^n) is divisible by a-b}
  (16^2004-1^2004) divisible by (16+1_=17 {by rule (a^n-b^n)is divisible by a+b}
  again,
  (20^2004-1^2004) divisible by (20-1)=19 {rule used above}
  (16^2004-3^2004) divisible by (16+3)=19 {rule used above)
  so, 17*19=323 ans.....
• 10 years agoHelpfull: Yes(0) No(0)