MathDB

4

Part of 2013 Hanoi Open Mathematics Competitions

Problems(2)

A even not divisible by 10, last 2 digits of A^20 (HOMC 2013 J Q4)

Source:

7/25/2019
Let AA be an even number but not divisible by 1010. The last two digits of A20A^{20} are:
(A): 4646, (B): 5656, (C): 6666, (D): 7676, (E): None of the above.
lastDigitsnumber theory
x_n=[(n+1)a]-[na], a=\sqrt{2013/2014} (HOMC 2013 Q4)

Source:

7/30/2019
Let x0=[a],x1=[2a]−[a],x2=[3a]−[2a],x3=[3a]−[4a],x4=[5a]−[4a],x5=[6a]−[5a],...,x_0 = [a], x_1 = [2a] - [a], x_2 = [3a] - [2a], x_3 = [3a] - [4a],x_4 = [5a] - [4a],x_5 = [6a] - [5a], . . . , where a=20132014a=\frac{\sqrt{2013}}{\sqrt{2014}} .The value of x9x_9 is:
(A): 22 (B): 33 (C): 44 (D): 55 (E): None of the above.
Sequencealgebrafloor function