1,148 reputation
316
bio website
location Turku, Finland
age 25
visits member for 1 year, 11 months
seen 4 hours ago

Mathematics student with a lot of interest to computer sciences and statistics.


Oct
17
revised Does every sequence of rationals, whose sum is irrational, have a subsequence whose sum is rational
k to n
Sep
24
awarded  Autobiographer
Jul
16
comment Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Well, you answered the title question :) I guess I wasn't really clear...The whole question should be more like, if p is a prime and the distance of a*p to the next largest square is itself a square, then the smallest a is of the form (p-2k) and the distance is k^2. In other words, if p is a prime and k is greater than what you gave in your answer, then the distance of p(p-2k) to the next largest square is never a square itself.
Jul
16
accepted Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Jul
16
comment Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
But you answered the title question, I think I can use that as well. Thank you.
Jul
16
comment Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Well, let me demonstrate how this fails if p is not a prime. Let p = 4141 = 41*101. Then 4141*3 + 11^2 = 112^2 and 4141*3 = 112^2-11^2. Then (112+11)/3 = 41. Also 3 = (4141 - 2*2069). But, for example, (4141 - 2*2068) = 5 and the next square of 4141*5 =144^2 and the distance is 31, which is not a square. So what I really wish to prove is that if p is a prime, this kind of thing cannot happen.
Jul
16
revised Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Explained the title
Jul
16
revised Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Explained the title
Jul
16
asked Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$
Jul
5
comment Maximum length of a representation of a number as an alternating sum of squares
@TonyK Yes, I think that is probably the smallest such n. I calculated it myself just a few minutes ago.
Jul
5
accepted Maximum length of a representation of a number as an alternating sum of squares
Jul
5
comment Maximum length of a representation of a number as an alternating sum of squares
@KarolisJuodelė You essentially answered my question and gave me a way to find a counterexample. If you could formulate this as a proper answer, I could give you the points.
Jul
5
revised Maximum length of a representation of a number as an alternating sum of squares
edited title
Jul
5
comment Maximum length of a representation of a number as an alternating sum of squares
@KarolisJuodelė Ah, yes. You are right. The numbers needed to get 9 are just huge, though. Kn of 89999999999999999999100000008999154 is 9....
Jul
5
revised Maximum length of a representation of a number as an alternating sum of squares
edited title
Jul
5
asked Maximum length of a representation of a number as an alternating sum of squares
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
26
reviewed Reviewed Drawing previously undrawn cards from a deck
Jun
26
reviewed Reviewed I need help with trying to answer this question. I know I have to find the derivative; but I do not know what to do after that.