Question

in base ten, the two-digit prime N is 45 more than the number formed by reversing the digits of N, find all the possible values of N.

Answer 1

Let $N=10x+y$, so that $x$ is the digits in the tens place and $y$ is the digit in the ones place. (Clearly $x\neq0$.)

$10x+y=45+10y+x\implies 9x-9y=45\implies x-y=5$

There are five possible two digits integers that satisfy this relation:

$x=5,y=0\implies N=50$
$x=6,y=1\implies N=61$
$x=7,y=2\implies N=72$
$x=8,y=3\implies N=83$
$x=9,y=4\implies N=94$

But the first, third, and fifth candidates are even, so they are not prime. The remaining are prime, however, so $N=61$ or $N=83$.