Show that 2903n - 803n - 464n + 261n is divisible by 1897.
Solution
Note that 1897 = 7·271. Since 7 and 271 are relatively prime (indeed both prime), it is sufficient to show that the expression is always divisible by 7 and always divisible by 271. We use the fact that a-b divides an-bn. Note that 2903 - 803 = 2100 which is a multiple of 7. It is eash to check that 464 - 261 is also a multiple of 7. The only other choice is 2903 - 464 and 803 - 261 and it is easy to check that they are multiples of 271.
© John Scholes
jscholes@kalva.demon.co.uk
29 Oct 2003
Last corrected/updated 29 Oct 03