MathDB

3

Part of 2013 Hanoi Open Mathematics Competitions

Problems(2)

largest integer [(n+1)a]-[na], a=\sqrt{2013}/\sqrt{2014} (HOMC 2013 J Q3)

Source:

7/25/2019
The largest integer not exceeding [(n+1)a]−[na][(n+1)a]-[na] where nn is a natural number, a=20132014a=\frac{\sqrt{2013}}{\sqrt{2014}} is:
(A): 11, (B): 22, (C): 33, (D): 44, (E) None of the above.
floor functionalgebra
8x^3 +6x - 1, x=1/2(\sqrt[3]{2+\sqrt5}+\sqrt[3]{2-\sqrt5}) (HOMC 2013 Q3)

Source:

7/30/2019
What is the largest integer not exceeding 8x3+6x−18x^3 +6x - 1, where x=12(2+53+2−53)x =\frac12 \left(\sqrt[3]{2+\sqrt5} + \sqrt[3]{2-\sqrt5}\right) ?
(A): 11, (B): 22, (C): 33, (D): 44, (E) None of the above.
floor functionpolynomialalgebra