# Best way to determine if number is triangular number?

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Richard Crozier on 6 Sep 2012
Hello,
I would like to test if an integer is a triangular number, and am wondering what the best way to achieve this is. I am aware that a triangular number is given by
x = n(n+1)/2
And that x is triangular if and only if 8x + 1 is a square.
However, what is the best way to actually test this in Matlab, giving consideration to floating point arithmetic?
I can think of methods like:
check x is an integer find if sqrt(8x + 1) is an integer to some floating point error
but there must be better ways.
##### 2 CommentsShowHide 1 older comment
Richard Crozier on 6 Sep 2012
I will only need this for relatively small numbers, it's actually a test of some user input. Useful to bear in mind though, thanks.

Matt Fig on 6 Sep 2012
istri = @(x) floor(sqrt(8*x+1))==sqrt(8*x+1);
x = 1:20;
idx = istri(x)
x(idx)
Richard Crozier on 6 Sep 2012
I think this is the best for my purposes, thanks!

Azzi Abdelmalek on 6 Sep 2012
Edited: Azzi Abdelmalek on 6 Sep 2012
k=0
for n=1:100 %for example
x = n*(n+1)/2;
y=sqrt(8*x+1);
if round(y)==y
k=k+1;
result(k)=x
end
end
n=size(result) % you will obtain n=100, which verify the formula
or
n=1:100 %for example
x = n.*(n+1)/2;y=sqrt(8*x+1)
all(y==round(y)) % if the result is 1, the formula is checked

Sean de Wolski on 6 Sep 2012
##### 2 CommentsShowHide 1 older comment
Sean de Wolski on 6 Sep 2012
Sure you can! You just have to get addicted to it and solve a bunch of other problems first!

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