MathDB

Cyclic Expression Equals Two

Source: Indian RMO 2013 Paper 1 Problem 4

2/1/2014

Find the number of

10

-tuples

(a_1,a_2,\dots,a_9,a_{10})

of integers such that

|a_1|\leq 1

and

a_1^2+a_2^2+a_3^2+\cdots+a_{10}^2-a_1a_2-a_2a_3-a_3a_4-\cdots-a_9a_{10}-a_{10}a_1=2.

modular arithmeticcombinatorics unsolvedcombinatorics

Indian RMO- Paper -3

Source: RMO - problem 4

12/11/2013

A polynomial is called Fermat polynomial if it can be written as the sum of squares of two polynomials with integer coefficients. Suppose that

f(x)

is a Fermat polynomial such that

f(0)=1000

. Prove that

f(x)+2x

is not a fermat polynomial

algebrapolynomialquadraticsmodular arithmeticnumber theory unsolvednumber theory

Indian RMO - Paper -4[4]

Source:

12/12/2013

Let

x

be a non-zero real numbers such that

x^4+\frac{1}{x^4}

and

x^5+\frac{1}{x^5}

are both rational numbers. Prove that

x+\frac{1}{x}

is a rational number.

Auxiliary Lines in a Triangle

Source: Indian RMO 2013 Mumbai Region Problem 4

2/1/2014

In a triangle

ABC

, points

D

and

E

are on segments

BC

and

AC

such that

BD=3DC

and

AE=4EC

. Point

P

is on line

ED

such that

D

is the midpoint of segment

EP

. Lines

AP

and

BC

intersect at point

S

. Find the ratio

BS/SD

.

ratiogeometry unsolvedgeometry

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