- Is it true that for every given set of integers (p,q,r) with min(p,q,r)>1 and max(p,q,r)>2 equation of the form

a^p + b^q = c^r

has no more than finite number of solutions in positive integers (a, b, c)?

Regards,

Andrey

[Non-text portions of this message have been removed] > Is it true that for every given set of integers (p,q,r) with min(p,q,r)>1 and max(p,q,r)>2 equation of the form

I mean distinct positive integers (a, b, c).

>

> a^p + b^q = c^r

>

> has no more than finite number of solutions in positive integers (a, b, c)?

Indeed, e.g., (n^2-1)^3 + (n^2-1)^2 = (n^3-n)^2 form an infinite number of solutions for (p,q,r) = (3,2,2).

Best regards,

Andrey

[Non-text portions of this message have been removed]- Andrey Kulsha wrote:
> Is it true that for every given set of integers (p,q,r) with min(p,q,r)>1 and max(p,q,r)>2 equation of the form

See the Fermat-Catalan conjecture.

>

> a^p + b^q = c^r

>

> has no more than finite number of solutions in positive integers (a, b, c)?

>

http://mathworld.wolfram.com/Fermat-CatalanConjecture.html