1.2

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

2011x^3 +ax^2 +bx+c = 0 if a+ b + c = 2010 \cdot 2011

Source: 2011 Saudi Arabia Pre-TST November 1.2

Find all triples

(a, b, c)

of integers such that

a+ b + c = 2010 \cdot 2011

and the solutions to the equation

2011x^3 +ax^2 +bx+c = 0

are all nonzero integers.

q_1^4+q_2^4+q_3^4+q_4^4+q_5^ is product of 2 even consecutive

Source: 2011 Saudi Arabia Pre-TST February 1.2

Find all primes

q_1, q_2, q_3, q_4, q_5

q_1^4+q_2^4+q_3^4+q_4^4+q_5^4

is the product of two consecutive even integers.