Hello mathematicians, puzzlers, and other curious people!
A conjecture came up in a homeschool group the other day. The student had been doing the kind of thing we believe in around here, looking for patterns in numbers, and noticed that the first several \”even powers of 2\” — by which they meant 2 raised to a power which is an even number, rather than an even number which is a power of 2 (which would include almost all powers of 2) — are perfect squares.
The student\’s mother wanted to know how the student could investigate further into whether this will always happen. Several of us had some feedback for them, but before I tell you what I came up with, take a little time to investigate it yourself and try to decide, with reasoning behind it, whether 
where n is even will always be a square number.
Calc You Later!
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