1

Part of 2019 May Olympiad

Problems(2)

9 always remainder by 1-10 May Olympiad (Olimpiada de Mayo) 2019 L2 P1

Source:

A positive integer is called piola if the

9

is the remainder obtained by dividing it by

2, 3, 4, 5, 6, 7, 8, 9

10

and it's digits are all different and nonzero. How many piolas are there between

1

100000

number theoryremainder

two-digit square

Source: May Olympiad 2019 L1 P1

Find all the two-digit numbers

\overline{ab}

that squared give a result where the last two digits are

\overline{ab}