I've aaready seen the same error somewhere else. a = x^(y/2) and b = y^(x/2) and then a + b and a - b are not necessary integers, so when you have (a + b).(a - b) = 17.1 = 1.17, it is not necessary that a + b = 17 and a - b = 1 (or a + b = 1 and a - b = 17). Find one solution with this method is a hazard. Besides, the fact that the other solution x = 1 and y = 16 is not found here is sufficient to prove that this method is not rigorous. A rigorous way to solve this problem is not evident at all, first prove that x and y are relatively small integers and then test all possibilities.
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If you include negative integers, there's a second solution: x=1 and y=-16.
I've aaready seen the same error somewhere else.
a = x^(y/2) and b = y^(x/2) and then a + b and a - b are not necessary integers, so when you have (a + b).(a - b) = 17.1 = 1.17, it is not necessary that a + b = 17 and a - b = 1 (or a + b = 1 and a - b = 17). Find one solution with this method is a hazard.
Besides, the fact that the other solution x = 1 and y = 16 is not found here is sufficient to prove that this method is not rigorous.
A rigorous way to solve this problem is not evident at all, first prove that x and y are relatively small integers and then test all possibilities.
Isn't x supposed to be greater than y? x=3 and y=4 is then wrong.
you assume that sqrt(x^y) is integer which is not true or proved