Let N be a positive integer not equal to 1. Then note that none of the numbers 2, 3, ... , N is a divisor of (N! -1). From this we can conclude that: (A) (N! - 1) is a prime number; (B) at least one of the numbers N+1 , N+2 , ...., N! […]
Let N be a positive integer not equal to 1. Then note that none of the numbers 2, 3, ... , N is a divisor of (N! -1). From this we can conclude that: (A) (N! - 1) is a prime number; (B) at least one of the numbers N+1 , N+2 , ...., N! […]
The number $1000! = 1.2.3...1000$ ends exactly with (A) $249$ zeroes; (B) $250$ zeroes; (C) $240$ zeroes; (D) $200$ zeroes; Discussion: To find the number of zeroes at the end of n! we just need to figure out the number of 5's occurring in prime factorization of it. Why? Because there are much more 2's […]
This post consists of Problems and solutions from TIFR 2013 Paper. Try to solve them and then read their solutions. TIFR 2013 Paper PART A (Linear and Abstract Algebra) Problem 1 Problem 2 - Automorphism of the Additive Group of Rationals Problem 3 - Existence of Real Root Problem 4 - Existence of Complex Root […]
This is an (ever-growing and ever-changing) list of books, useful for school and college mathematics students. If you are working toward Math Olympiad, I.S.I., C.M.I. entrance programs or intense college mathematics, these books may prove to be your best friend. If you are taking a Cheenta Advanced Math Program, chances are that you will referred […]
Let's discuss this objective problem number 14 from ISI BStat BMath. Try to solve the problem and then read their solution. Problem 14 f(x) = tan(sinx) (x > 0) To understand the graph of a function, easiest and the most proper method is to apply techniques from calculus. We will quickly compute, derivative and second […]
This post contains the six Indian National Maths Olympiad, INMO 2015 problems. Try to solve these problems. Let ABC be a right-angled triangle with $ \angle{B}=90^{\circ} $. Let BD is the altitude from B on AC. Let P, Q and Ibe the incenters of triangles ABD, CBD, and ABC respectively. Show that circumcenter of triangle […]
Let's understand the factor method of Diophantine equations step-by-step. Aso, try the question related to it. Diophantine Equations Consider an equation for which we seek only integer solutions. There is no standard technique of solving such a problem, though there are some common heuristics that you may apply. A simple example is $ x^2 - […]
Here is an excerpt from an email conversation that I had with one of our student's parent: "While we have lots of books with problems, the one challenge has been that problems in the books are not classified by level of difficulty or arranged in increasing order of difficulty. Much like a weight-lifter gradually increases […]
This is a session plan for 'Mathematics in Summer 2014'. (Venue: Scotland, Glasgow). Let's discuss Homological Triangles. Introduction to homological triangles, perspectivities. Menalaus' Theorem, Desargues Theorem Anti parallel lines, some examples of homological triangles, homothety as a special case of homology, cevian, orthic triangle, some basic properties of angle bisectors' Special Triangles and points: anti-supplemental […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Interior Angle.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Smallest positive Integer.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Proper divisors.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Algebraic value.
Try this beautiful problem from Probability based on dice from AMC-10A, 2011. You may use sequential hints to solve the problem
Try this beautiful problem from Geometry: Area of Region in a Circle from AMC-10A, 2011, Problem -18. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based smallest positive value from PRMO 2019. You may use sequential hints to solve the problem.
Try this beautiful problem from combinatorics based on Regular Polygon from PRMO 2019. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Positive solution.
Try this beautiful problem from PRMO, 2019, problem-12, based on Integer Problem. You may use sequential hints to solve the problem.