Download MATH 9 ASSIGNMENT 8: MATH BATTLE! 1. A teacher writes 10

MATH 9
ASSIGNMENT 8: MATH BATTLE!
MAR 29, 2015
1. A teacher writes 10 natural numbers on the board. Show that it is always possible to choose some
of them and put signs + and - between them so that the resulting expression is a multiple of 1001.
[Hint: such an expression can be written as A1 − A2 , where each Ai is a sum of some subset of the
original 10 numbers.]
2. Find the coefficient of x37 in
(a) (1 + x + x2 + ... + x100 )2
(b) (1 + x + x2 + ... + x100 )3
3. In the number 454**, find the missing digits so that the number is divisible by 2, by 7, and by 9.
4. Does there exist a polynomial P (x) with integer coefficients such that P (6) = 5 and P (14) = 9?