MathDB

19

Part of 2014 BMT Spring

Problems(2)

2014 BMT Team 19

Source:

1/6/2022
A number kk is nice in base bb if there exists a kk-digit number nn such that n,2n,...knn, 2n, . . . kn are each some cyclic shifts of the digits of nn in base bb (for example, 22 is nice in base 55 because 2⋅135=3152\cdot 135 = 315). Determine all nice numbers in base 1818.
number theory
BMT 2014 Spring - Individual 19

Source:

1/22/2022
Evaluate the integral ∫0π/2tan⁡θdθ\int_0^{\pi/2} \sqrt{\tan \theta} d\theta.
calculusintegration