4

Part of 2015 CHMMC (Fall)

Problems(2)

2015 Fall Team #4

Source:

P(x) = x^{16}-x^{15}+·...-x+ 1

, and let p be a prime such that

p-1

is divisible by

34

p = 103

is an example). How many integers a between

1

p-1

inclusive satisfy the property that

P(a)

is divisible by

p

number theoryalgebra

2015 CHMMC Tiebreaker 4 , 46, 656, 000, 000 = product of divisors of n

Source:

The following number is the product of the divisors of

n

46, 656, 000, 000

n

number theoryCHMMC