EGMO 2014, Problem 3. We denote the number of positive divisors of a positive integer \(m\) by \(d(m)\) and the number of distinct prime divisors of \(m\) by \(\omega(m)\). Let \(k\) be a positive integer. Prove that there exist infinitely many positive integers \(n\) such that \(\omega(n) = k\) and \(d(n)\) does not divide \(d(a^2+b^2)\) for any positive integers \(a, b\) satisfying \(a + b = n\).
Women in Mathematics beyond Stereotypes — Sylvia Serfaty
We continue our series on women in mathematics who defy the usual mathematicians' stereotypes with Sylvia Serfaty, who does not see herself as a genius or a nerd.
Continuiamo questa serie su matematiche che non corrispondono ai consueti stereotipi sui matematici con Sylvia Serfaty, che non si ritiene né un genio, né un nerd.
Photo: © Julien Jouanjus
Thinking Out Loud – EGMO 2014 Problem 2
EGMO 2014, problem 2. Let \(D\) and \(E\) be points in the interiors of sides \(AB\) and \(AC\), respectively, of a triangle \(ABC\), such that \(DB=BC=CE\). Let the lines \(CD\) and \(BE\) meet at \(F\). Prove that the incentre \(I\) of triangle \(ABC\), the orthocentre \(H\) of triangle \(DEF\) and the midpoint \(M\) of the arc \(BAC\) of the circumcircle of triangle \(ABC\) are collinear.
Women in Mathematics beyond Stereotypes — Gigliola Staffilani
In this series of posts we would like to talk about women in mathematics who are not as well known as, say, Hypatia or Emmy Noether, and are at the same time quite different from the usual mathematicians' stereotypes. This week we have the story of Gigliola Staffilani: from a farm in Italy to MIT.
In questa serie di post vorremmo parlare di matematiche meno famose di, ad esempio, Ipazia o Emmy Noether e che, allo stesso tempo, non corrispondono ai consueti stereotipi sui matematici. Questa settimana abbiamo la storia di Gigliola Staffilani: da una fattoria abruzzese al MIT.