Question 771731
Let {{{ t }}} = the tens digit
Let {{{ u }}} = the units digit
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{{{ t^2 + 10u = u^2 + 10t }}}
{{{ t^2 - u^2 = 10t - 10u }}}
{{{ ( t - u )*( t + u ) = 10*( t - u ) }}}
Divide both sides by {{{ t - u }}}
{{{ t + u = 10 }}}
The combinations where both digit
are prime are:
------------
t,u
---
1,9
9,1
7,3
3,7
5,5
----
check:
37
{{{ t^2 + 10u = u^2 + 10t }}}
{{{ 7^2 + 10*3 = 3^2 + 10*7 }}}
{{{ 49 + 30 = 9 + 70 }}}
{{{ 79 = 79 }}}
OK- you can check the others