Triangle numbers are :
1,3,6,10,15,21,28.
Somebody tells you a random positive integer of any size. Is there a quick way to work out if it is a triangle number or not (in other words, without going through all of the triangle numbers untill you get to a number as high or higher as the integer you've been told)?
I worded my previous post very poorly. Sorry.
Yes, I understand that 2n is even and that 2n+1 is odd when n is an int.
It is because of this that you'll see only the odd squares and never the evens coming up. Which is what I was trying so clumsily to point out.
Take the rand. pos. int. that you were given, and multiply it by eight;
then add one to this. If the result is a perfect square, then
the rand.pos. int. your were given is a triangle number.
Note - this perfect square will only be odd - you'll never have an even here.
You have 3^2 but not 4^2; you have 5^2 but not 6^2; you have 7^2 but not 8^2 & so on.
1 is a tri nbr because 1 + 8(1) = 9 = 3^2
3 is a tri nbr because 1 + 8(3) = 25 = 5^2
6 is a tri nbr because 1 + 8(6) = 49 = 7^2
10 is a tri nbr because 1 + 8(10) = 81 = 9^2
15 is a tri nbr because 1 + 8(15) = 121 = 11^2
21 is a tri nbr because 1 + 8(21) = 169 = 13^2
28 is a tri nbr because 1 + 8(28) = 225 = 15^2
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