MathDB

Let

n_1 = \overline{abcabc}

and

n_2= \overline{d00d}

be numbers represented in the decimal system, with

a\ne 0

and

d \ne 0

.
a) Prove that

\sqrt{n_1}

cannot be an integer. b) Find all positive integers

n_1

and

n_2

such that

\sqrt{n_1+n_2}

is an integer number. c) From all the pairs

(n_1,n_2)

such that

\sqrt{n_1 n_2}

is an integer find those for which

\sqrt{n_1 n_2}

has the greatest possible value

Problem Statement