Cute NT ^-^
Posted: Sun Apr 25, 2021 9:43 am
Find all positive integers $x,a,b$ such that $x^a+x^b=x^{a+b}$
Solution:
Solution:
$x^{a} × x^{b} = x^{a+b}$
If $x^{a} = m,x^{b} = n$. Then,
$m + n = mn$
$n = m(n-1)$
Then $n-1 = 1 \rightarrow n=2$
It follows that $m=2$
So only solution $(x,a,b)=(2,1,1)$