MathDB

algebra problem

Source: Netherlands TST for IMO 2017,day 1 problem 3

2/1/2018

let

x,y

be non-zero reals such that :

x^3+y^3+3x^2y^2=x^3y^3

find all values of

\frac{1}{x}+\frac{1}{y}

algebra

pable numbers

Source: Netherlands TST for IMO 2017 day 2 problem 3

2/1/2018

Let

k > 2

be an integer. A positive integer

l

is said to be

k-pable

if the numbers

1, 3, 5, . . . , 2k - 1

can be partitioned into two subsets

A

and

B

in such a way that the sum of the elements of

A

is exactly

l

times as large as the sum of the elements of

B

. Show that the smallest

k-pable

integer is coprime to

k

.

number theory

easy NT problem

Source: Netherlands TST for IMO 2017 day 3 problem 3

2/1/2018

Compute the product of all positive integers

n

for which

3(n!+1)

is divisible by

2n - 5

.

number theory

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