Finding number of positive integral solutions of $x^4-y^4=3879108$ Find the number of positive integral solutions of $$x^4-y^4=3879108$$ $$3879108=36*277*389$$
I tried simplifying factors of $3879108$ to get terms in the form of $x^4-y^4$. However, I am unable to proceed. Do the (positive integral) solutions exist, and if yes, how to obtain them?

A broad hint: first of all, it's clear that $x$ and $y$ must have the same parity (why?).  If $x$ and $y$ are both even, then $x^4$ and $y^4$ are both divisible by $16$, and so their difference must also be.  Suppose instead that $x$ and $y$ are both odd.  Now, $x^4 = \left(x^2\right)^2$, and likewise $y$; what do you know about squares of odd numbers?  (Alternately, as suggested in the comments: you can factor $x^4-y^4 = (x-y)(x+y)(x^2+y^2)$; now, look at the parity of the terms on the RHS.)
