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Pell Mell
Submitted by Billy from Montreal, QC, 3/4/2000. Original answer by Carl Johan Ragnarsson; this article by Allen Stenger.
Show that for any
the number
can be written as the
difference of the square roots of two consecutive integers.
Hint 1
Work out the first few powers and verify the result for them. Do you see any patterns?
Want another hint? Click here.
Click here for the complete solution.