MathDB

Consider the set

E

consisting of pairs of integers

(a, b)

, with

a \geq 1

and

b \geq 1

, that satisfy in the decimal system the following properties:
(i)

b

is written with three digits, as

\overline{\alpha_2\alpha_1\alpha_0}

\alpha_2 \neq 0

;
(ii)

a

is written as

\overline{\beta_p \ldots \beta_1\beta_0}

for some

p

;
(iii)

(a + b)^2

is written as

\overline{\beta_p\ldots \beta_1 \beta_0 \alpha_2 \alpha_1 \alpha_0}.

Find the elements of

E

Problem Statement