Advanced Search

The equation $3^a+5^b-7^c=1$, to be solved in non-negative rational integers $a,b,c$, has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation $y^2=3^a+2^b+1$, to be solved in non-negative rational integers $a,b$ and a rational integer $y$, has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.