9

Part of 2024 JHMT HS

Problems(2)

Last Two Digits and 21st Power

Source:

N \in \{10, 11, \ldots, 99\}

be a two-digit positive integer. Compute the number of values of

N

for which the last two digits in the decimal expansion of

N^{21}

are the digits of

N

in the same order.

number theory2024

Area Involving Minimum and Sum of Squares

Source:

Compute the smallest positive integer

k

such that the area of the region bounded by

k\min(x,y)+x^2+y^2=0

100