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Find all triples of integers $(x,y,d)$ with $d\ge 3$ such that $x^2+4=y^d$.

I did some advance in the problem with Gaussian integers but still can't finish it. The problem is similar to Catalan's conjecture.

NOTE: You can suppose that $d$ is a prime.

Source: My head

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    Trivial observation: if $d$ is even there is no nontrivial solution.2012-03-11
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    I'm wondering, why is the tag `(complex-numbers)` used here? The problem is asking for integer solutions to an integer polynomial.2012-03-11
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    @J.D. Probably b/c OP approached it using $\mathbb Z[i]$.2012-03-11
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    The case $d=3$ is solved as Example 4.1.4 in the book An Introduction to Diophantine Equations: A Problem-Based Approach by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu, [p. 157](http://books.google.com/books?id=D_XmfolL-IUC&pg=PA157).2012-03-26

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