MathDB

Romania TST 2016 Day 2 P1

Source: Romania TST 2016 Day 2 P1

11/1/2017

Given positive integers

k

and

m

, show that

m

and

\binom{n}{k}

are coprime for infinitely many integers

n\geq k

.

number theory

Romania TST 2016 Day 3 P1

Source: Romania TST 2016 Day 3 P1

11/1/2017

Given a positive integer

n

, determine all functions

f

from the first

n

positive integers to the positive integers, satisfying the following two conditions: (1)

\sum_{k=1}^{n}{f(k)}=2n

; and (2)

\sum_{k\in K}{f(k)}=n

for no subset

K

of the first

n

positive integers.

algebranumber theory

Equilateral in plane

Source: Romania TST 2016 Day 4 Problem 1

6/2/2016

Determine the planar finite configurations

C

consisting of at least

3

points, satisfying the following conditions; if

x

and

y

are distinct points of

C

, there exist

z\in C

such that

xyz

are three vertices of equilateral triangles

combinatorics

\frac{x^2+y}{xy+1}

Source: Romania TST 2016 Day 5 Problem 1

6/2/2016

Determine the positive integers expressible in the form

\frac{x^2+y}{xy+1}

, for at least

2

pairs

(x,y)

of positive integers

number theory

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