Understand the Problem: The polynomial \(x^7+x^2+1\) is divisible by (A) \(x^5-x^4+x^2-x+1\) (B) \(x^5-x^4+x^2+1\) (C) \(x^5+x^4+x^2+x+1\) (D) \(x^5-x^4+x^2+x+1\) Solution A shorter solution or approach can always exist. Think about it. If you find an alternative solution or approach, mention it in the comments. We would love to hear something different from you. Also Visit: I.S.I. & C.M.I […]
ISI - CMI entrance book list is useful for B.Stat and B.Math Entrance of Indian Statistical Institute, B.Sc. Math Entrance of Chennai Mathematical Institute
A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!
Hello mathematician! I do not like homework. They are boring ‘to do’ and infinitely more boring to ‘create and grade’. I would rather read Hilbert’s ‘Geometry and Imagination’ or Abanindranath’s ‘Khirer Putul’ at that time. Academy Award winner Michael Moore, Rabindranath Tagore and Finland’s educators (who have the number 1 education system for school students) are […]
Do you want to invent new numbers and new functions? The story of how any age old banking formula led to the discovering of real analysis!
The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.
This is an I.S.I. Entrance Solution Problem: P is a variable point on a circle C and Q is a fixed point on the outside of C. R is a point in PQ dividing it in the ratio p:q, where p> 0 and q > 0 are fixed. Then the locus of R is (A) […]
This is a problem from ISI B.Stat-B.Math Entrance Exam 2018, Subjective Problem 7. It is based on Bases, Exponents and Role reversals. I.S.I. Entrance 2018 Problem 7 Let $(a, b, c)$ are natural numbers such that $(a^{2}+b^{2}=c^{2})$ and $(c-b=1)$. Prove that(i) a is odd.(ii) b is divisible by 4(iii) $( a^{b}+b^{a} )$ is divisible by […]
Try this beautiful Integer-based Problem from Algebra from PRMO 2018, Question 20. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra, based on Sum of two digit numbers from PRMO 2016. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-Regional Mathematics Olympiad, PRMO, 2014, based on finding side of Triangle. You may use sequential hints.
Try this beautiful problem from Geometry: The area of a trapezoid from AMC-8 (2003). You may use sequential hints to solve the problem.
Try this beautiful problem from AMC 8, 2003, problem no-22 based on Largest area. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry, based on Cube from AMC-10A, 2007. You may use sequential hints to solve the problem
Try this problem from Geometry: Ratios of the areas of Triangle and Quadrilateral from AMC-10A, 2005 You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Angles and Triangles.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Digits and Numbers.
Try this beautiful problem from Geometry based on Try this beautiful problem from Algebra based on Largest Common Divisor . from PRMO 2014. You may use sequential hints to solve the problem.