by Ashani Dasgupta

RMO 2018 Tamil Nadu Problem 3 is from Number Theory. We present sequential hints for this problem. Do not read all hints at one go. Try it yourself. Problem Show that there are infinitely many 4-tuples (a, b, c, d) of natural numbers such that \( a^3 + b^4 + c^5 = d^7... by Ashani Dasgupta

RMO 2018 Tamil Nadu Problem 2 is from Theory of Equations. We present sequential hints for this problem. Do not read all hints at one go. Try it yourself. Problem Find the set of all real values of a for which the real polynomial equation \( P(x) = x^2 – 2ax + b... by Ashani Dasgupta

RMO 2018 Tamil Nadu Problem 1 is from Geometry. We present sequential hints for this problem. Do not read all hints at one go. Try it yourself. Problem Let ABC be an acute-angled triangle and let D be an interior point of the line segment BC. Let the circumcircle of... by Ashani Dasgupta

RMO2018 Tamil Nadu Solutions (Sequential Hints) and related discussion follows. This is a work in progress. Also see Advanced Math Olympiad Program Let ABC be an acute-angled triangle and let D be an interior point of the line segment BC. Let the circumcircle of... by Ashani Dasgupta

The golden ratio is arguably the third most interesting number in mathematics. The first two slots are of course reserved for \( \pi \) and \( e \). Among other things, golden ratio has the uncanny habit of appearing unexpectedly in nature and geometry. What is golden... by Ashani Dasgupta

Consider the following problem: Problem Show that there do no exist non-negative integers k and m such that \( k! + 48 = 48(k+1)^m \) Discussion Claim 1: \( k \geq 9 \) If there are such integers then \( k! = 48 \times ((k+1)^m – 1 )\). Expanding we have \( k! =...