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Conjecture: Let $a_1, a_2, \cdots , a_n>0$ and $y \ge x $ then $$(a_1^x+a_2^x+\cdots+a_n^x)^y \ge (a_1^y+a_2^y+\cdots+a_n^y)^x$$ Equality iff $x=y$ Is the conjecture right? Have you ever seen this ...

This is a simple question about terminology and provenance. I just need to sort out the circle of conjectures that generalize and refine the twin prime conjecture. I've encountered Polignac's ...