If you view it as a right triangle with one leg equal to 1 and the other 1727*y^2, the difference between the hypotenuse and the longer leg is about 1...

Well, I did read the paper and it is high-level stuff. It's loosely related to the Pell equation, but the media made it seem (to me at least) that the...

@john-nolton You know, I hate to be a doubting Thomas (well, not really) but if you go here, you'll find a widget added to Wolfram Alpha in 2010 that...

Well, I have an answer by applying the principle of cheating. Enter 1729 At this website: I don't know where Dave got the problem, but here's one d...

@bill93 That's what I got, but the products don't work as the did for the example. Maybe there are others that work for all three factors.

@spmpls Yep. Surveyors are smart and don't waste time on nonproductive pursuits. We old teachers mess with stuff like this because it sometimes leads...

@bill93 It may not even lead to a solution. The factor 7 has at least 2 solutions, 3 and 48. Neither will combine with either of the other two factor...

OK, so 13*180^2+1 = 421,201 and sqrt(421,201) = 649. 650*648 = 421,200. That leaves 19 to be done.

@bill93 I don't see anything obviously wrong, but consider using an old problem-solving technique: solving a simpler problem. Consider 5*y^2+1 = u^2...

@flga-2-2 Well, there's no BS in the dungeon, unless it's in the food. ?ÿ

@bill93 Can you prove that "With large y there can be no grouping of the factors on the left side into two values that differ by only 2."? Consider ...

@mike-marks I think it's something like 6 or 7 decimal places of Pi required to navigate across the solar system, but that may not be enough to ident...

@mike-marks You have to use the full precision calculator and set the number of decimal places you want in the little box below the "history" box. So...

Kind of interesting to note that the problem can be cast as a right triangle with legs y*sqrt(1729) and 1 and hypotenuse sqrt(1729*y*y +1). One acute...

@holy-cow Factorials and powers of 2 are staples of prime number hunters. A lot of cryptography is based on numbers that are not prime but are next t...

@mike-marks The square root of 2^668122 is just 2^334061; take half the exponent. But, we want 1729*y^2+1 to be a perfect square and your y produces ...

@bill93 Not mine, either. I'd be a bad choice for a crypto job.

Not quite. That number is actually 447685271124000.969078681, truncated at 9 decimal places. This site may have enough capacity to find the answer, o...

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