1

Part of 2022 Puerto Rico Team Selection Test

Problems(2)

3x3 system Puerto Rico TST 2022.1.1

Source:

Find all triples

(a, b, c)

of positive integers such that:

a + b + c = 24

a^2 + b^2 + c^2 = 210

abc = 440

algebrasystem of equationsnumber theory

2022-digit interesting numbers of Puerto Rico TST 2022.2.1

Source:

Let's call a natural number interesting if any of its two digits consecutive forms a number that is a multiple of

19

21

. For example, The number

7638

is interesting, because

76

is a multiple of

19

63

21

38

is a multiple of

19

. How many interesting numbers of

2022