2 last digits

Number Theory Level 4

A 2-digit integer $\overline{ab}$ is called " beautiful " if:

$\overline{ab}$ is a prime.
There is a square has 2 last digits is $\overline{ab}$

Find the sum of possible values of $\overline{ab}$ .

Note: $a$ can be equal $0$ .

The answer is 220.

1 solution

展豪張
Mar 23, 2016

First we check that if $\overline{02}$ can be a 'tail' of square, which clearly not.
So from $\overline{ab}$ is a prime, $b=1,3,7,9$ .
Since it is a tail of square, $b=1,9$ .
$\therefore a$ is even.
Check them all and we will have answer $=41+61+29+89=220$ .

2 last digits

The answer is 220.

1 solution

0 pending reports