A little mathematical puzzle

Question

ganeshie8 · Answer

We just need to get even parity i guess

dls · Answer

Its not true.
Suppose the given sequence is :
5 10 14 
In this case answer is 1.

ganeshie8 · Answer

Yeah, making everything even is just an upper bound. Not the least upper bound

dls · Answer

yes that is for sure :)

dls · Answer

Another example :
11 33 55 
answer would be 0 here.
PS : I am just considering already non decreasing sequences for now

dan815 · Answer

hey is it solved already?

dls · Answer

nope

dan815 · Answer

okay so 
n buckets, non decreasing order, GCD of partitions > 1

i have a question about the GCD of paritions

dan815 · Answer

are we talking about comaring all the paritions at once or the comparison of* 2 paritions at a time

dls · Answer

GCD of all the elements taken at once.
GCD(11,33,55) = 11

dan815 · Answer

kk

dan815 · Answer

cool question so i think we should be considering prime number seapaartiosn basically

dan815 · Answer

so lets take an example 
n=20

2*2*5, as it has only 3 prime factors there can only be 1 sequence

dan815 · Answer

for n bunckets

ganeshie8 · Answer

Let $\{a_n\}$ be the given sequence.

Let $\{b_n\}$ be the required sequence of extra balls.

Then we need to have $\gcd(a_1+b_1,a_2+b_2,\ldots,a_n+b_n ) \gt 1$,
 and  $\{a_n+b_n\}$ must be a non decreasing sequence.

dan815 · Answer

oh true we also have to consider the unknown balls in each bin first of all

dan815 · Answer

if they were all zero they have the trivial solution of simple adding by 2s in each bin

dls · Answer

Assume that minimum ball in each bin is >=1

ganeshie8 · Answer

$\gcd(p,q,r) = \gcd(\gcd(p,q),r)$

dan815 · Answer

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