Question

Total number of integral points lying inside the triangle formed by the lines \(xy=0\) and \(x+y=a\), where \(a\) is any positive integer.

Answer 1

i just wanna clear my doubts

for example xy=0 and x+y=3 one integral point inside this one ??

Answer 2

Yeah, I think so but I couldn't be sure either I got it on my test today.

Answer 3

a=3 1 points
a=4 1+2 points
a=5 1+2+3 points
...

Answer 4

For a = 21, 1 + 2 + 3 + ... + 19 = 19*20/2 = 190?

Answer 5

Thanks.

Answer 6

I happened to get the same but wasn't sure of it.