MathDB

15

Part of 2016 Hanoi Open Mathematics Competitions

Problems(2)

f(2014)=2015, f(2015)=2016, f(2013)- f(2016) prime (HOMC 2016 J Q15)

Source:

8/6/2019
Find all polynomials of degree 33 with integer coeffcients such that f(2014)=2015,f(2015)=2016f(2014) = 2015, f(2015) = 2016 and f(2013)āˆ’f(2016)f(2013) - f(2016) is a prime number.
polynomialIntegeralgebraprime
min T=42a^2+34b^2+43c^2 when 18ab+9ca+29bc=1 (HOMC 2016 S Q15)

Source:

9/8/2019
Let a,b,ca, b, c be real numbers satisfying the condition 18ab+9ca+29bc=118ab + 9ca + 29bc = 1. Find the minimum value of the expression T=42a2+34b2+43c2T = 42a^2 + 34b^2 + 43c^2.
inequalitiesalgebraminimum