10

Part of 2010 AIME Problems

Problems(2)

Source: AIME 2010I Problem 10

N

be the number of ways to write

2010

in the form 2010 \equal{} a_3 \cdot 10^3 \plus{} a_2 \cdot 10^2 \plus{} a_1 \cdot 10 \plus{} a_0, where the

a_i

's are integers, and

0 \le a_i \le 99

. An example of such a representation is 1\cdot10^3 \plus{} 3\cdot10^2 \plus{} 67\cdot10^1 \plus{} 40\cdot10^0. Find

N

Integer Quadratic

Source: 2010 AIME II #10

Find the number of second-degree polynomials

f(x)

with integer coefficients and integer zeros for which f(0)\equal{}2010.

quadraticsalgebrapolynomialcountingdistinguishabilityAMCUSA(J)MO