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Isolate integers in a pair from a table?

Posted 17 days ago
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Evening,

I am trying to isolate the whole numbers/integers from a pair of numbers within a range. This is the function I am currently using:

Table[{Sqrt[1 + 5 k^2], Sqrt[k^2]}, {k, 0, 500}]

I want to find out which of the Sqrt(1+5k^2) is a square number itself, so a whole number. I am currently having to try a range and read through all my results. What I would like to to use a command, or a different command to the above, to just show those results that give me whole numbers.

I hope I have explained that well enough and am asking in the right place. Thank you in advance.

4 Replies
Posted 17 days ago

Hi Emily,

Is this what you mean?

Table[{Sqrt[1 + 5 k^2], Sqrt[k^2]}, {k, 0, 500}] // Select[IntegerQ@First@# &]
(* {{1, 0}, {9, 4}, {161, 72}} *)
Posted 17 days ago

Yes!! Yes that is exactly it thank you! I was scouring Google for hours earlier today. Thank you so much!

Posted 16 days ago

There is usually more than one way to solve problems, this is another.

Cases[Table[{Sqrt[1 + 5 k^2], Sqrt[k^2]}, {k, 0, 500}], {a_, b_} /; 
  IntegerQ[a]]
Posted 16 days ago

Another variant:

Cases[Table[{Sqrt[1 + 5 k^2], Sqrt[k^2]}, {k, 0, 500}], {_Integer, _}]
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