#Number theory: is there any more solutions?
vernal hawk
indigo marsh
I think a more proper way is to show that the quadratic factor has no real solutions.
Or, wait, I'm sorry.
Also, you did your work wrong. m(m + 1)/2 is, so far as I know at least, only the formula for the sum of the natural numbers up to m.
That's why m = 0 yields 0.
I don't know why you just asserted m =/= 0.
vernal hawk
Also, you did your work wrong. m(m + 1)/2 is, so far as I know at least, only th...
thats all that the question asks for i believe
vernal hawk
I don't know why you just asserted m =/= 0.
because then it wouldnt represent adding up starting from 1
indigo marsh
thats all that the question asks for i believe
Is -1 a natural number?
vernal hawk
oh yeah, i mean that the m(m+1)/2 satisfies what the question asks for
it just says consecutive integers
doesnt specify anything else
indigo marsh
oh yeah, i mean that the m(m+1)/2 satisfies what the question asks for
But does it though? Like I just said, I think it only yields the sum of consecutive natural numbers.
vernal hawk
oh yeah ur right but after -1 the equation just mirrors what it does in the positive
idk if im making sense
but for every positive solution there is a negative one
sand basin
i swear u just use the quadratic formula no?
indigo marsh
No, the right side of the equation is simply incorrect.
vernal hawk
surely it doesnt matter because the equation works for all positive integers and if there is a positive solution then there is a negative one too
indigo marsh
No.
vernal hawk
explain please
indigo marsh
You're directly contradicting yourself.
Because you said -4 was a solution, but 4 is not.
Or -1 is a solution and 1 is not.
vernal hawk
for the right hand side
vernal hawk
Or -1 is a solution and 1 is not.
apart from that case
indigo marsh
So apart from literally the only case you bothered to directly investigate.
indigo marsh
I'm trying to help you.
I'm trying to help you break the bad habits of thinking that you're engaged in.
vernal hawk
acha
indigo marsh
Okay, so. When m >= 1, then yes, the sum of all consecutive integers from 1 to m is m(m + 1)/2.
But we need different math to account for when m < 1.
vernal hawk
right yes, but its not really that important because IF there is a positive solution then there WILL be a negative solution, not necessarily with the same magnitude of m
indigo marsh
Prove that.
indigo marsh
Which part?