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 Mar 24 answered Number of integer solutions $(x, y)$ of $x(x+6) = y^2 + k$ for different integer values of $k$ Mar 22 comment Mathematicians shocked(?) to find pattern in prime numbers This question brings together two things which don't have to go together: properties of primes, and properties of integers modulo 10. It may be helpful to ask the following simpler but related question: if a prime $>3$ is of the form $3n+1$, is it or is it not equally likely that the next larger prime is of the form $3n+1$ or $3n+2$? I suspect it is not equally likely, however large the numbers are, because if $3N+1$ is prime, the next possible prime - not divisible by 2 or 3 - is $3(N+1)+2$. This gives $3n+2$ an advantage which seems unlikely to be offset by other considerations. Mar 18 answered For every positive integer $n$, $n^2 + n +19$ is prime Mar 6 accepted Locus of Points $O$ such that $AO^3+BO^3=AB^3$ Mar 6 comment Locus of Points $O$ such that $AO^3+BO^3=AB^3$ Thank you, so as expected the point equidistant from A and B corresponding to $s=2^{1/3}$ is not constructible, but infinitely many other points can be constructed, the simplest having $s=3/2$ giving $a=(11/48)^{1/2}$. Mar 2 asked Locus of Points $O$ such that $AO^3+BO^3=AB^3$ Feb 12 comment Find a thousand natural numbers such that their sum equals their product @user230452 I've edited my answer to explain how the solution was found. Feb 12 revised Find a thousand natural numbers such that their sum equals their product To explain how solution found. Feb 11 revised Find a thousand natural numbers such that their sum equals their product Improve formatting Feb 11 awarded Yearling Feb 11 answered Find a thousand natural numbers such that their sum equals their product Sep 10 revised Integer pairs satisfying $(y-a)(y-b) = x^3$ Simplify reasoning to (2) Sep 10 answered Integer pairs satisfying $(y-a)(y-b) = x^3$ May 30 awarded Nice Answer May 24 accepted If $X$ has a Poisson distribution with $E[X]=\lambda$, does $Var[X^2]=4\lambda^3+6\lambda^2+\lambda$? May 22 comment If $X$ has a Poisson distribution with $E[X]=\lambda$, does $Var[X^2]=4\lambda^3+6\lambda^2+\lambda$? It is helpful, thank you ... but it's also fair to note that the more concise answers by Clement C. and Jack D'Aurizio were posted first. May 22 asked If $X$ has a Poisson distribution with $E[X]=\lambda$, does $Var[X^2]=4\lambda^3+6\lambda^2+\lambda$? Mar 31 awarded Necromancer Jan 3 comment Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$? My answer, although accepted, contained an error, now corrected by adding a minus sign before $(c^5+d^5+e^5)$. Jan 3 revised Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$? Correction to include missing minus sign.