These tables will be needed for some problems below.
Can a number of the form 200…009 (with some number of zeros between the twos and the nines) be a perfect square of an integer for any number of zeros?
Which digits can a perfect square end with?
Can the square of an integer have the form a) 5q + 2, b) 3q − 1, c) 6q − 1?
Take any positive integer n. Find the sum of its digits; then find the sum of digits of that result, and so on, until you get a single-digit number R. a) Prove that R is the remainder of n upon division by
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