Numbers of the form, where a > 1 are called generalized Fermat numbers. An odd prime p is a generalized Fermat number if and only if p is congruent to 1 (mod 4). (Here we consider only the case n>0, so 3 = is not a counterexample.)
By analogy with the ordinary Fermat numbers, it is common to write generalized Fermat numbers of the form as Fn(a). In this notation, for instance, the number 100,000,001 would be written as F3(10). In the following we shall restrict ourselves to primes of this form, .
If we require n>0, then Landau's fourth problem asks if there are infinitely many generalized Fermat primes Fn(a).
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