2 last digits

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

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

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

Note: a a can be equal 0 0 .


The answer is 220.

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1 solution

展豪 張
Mar 23, 2016

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


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