1$
$$k_1 = x_1 – k_2 -2k_3 = t - (3 – t – s ) – 2 s  = 2t – s – 3$$
So the solution is
$$(k_1, k_2, k_3) = (2t-s-3, 3-t-s,s) ;  \quad\forall s,t\in\mathbb Z$$
$s,t$ are arbitrary integers.
We can get solutions to positive integers just by apply restrictions to final 
solution.
$$s = 1,t=2 \implies (k_1, k_2, k_3) = (1,1,0)$$

But this is the primary solution algorithm.when we want to solve a bigger Diophantine equation we just need more variables to represent the final solution form, for Diophantine equation with n variables we need n-1 variable to represent the final solution and when our goal is to find the positive integer solutions we get to a mass number of limitations that is really hard to overcome.
Here's the second approach arrives, extensive and special case solution to positive integers.this approach instead of compacting to a simple equation form, try to decompose equation to parts that are isolated from each other and result to some smaller equations and especially is best for solutions in positive integer domain with application related to electronics and communications.my thesis was about design modern approaches algorithms to equations and implementation on devices.
This is part of my thesis that I worked hard on the algorithms on it.It's my pleasure to answer your request and send my work to share my knowledge and ideas.
you can contact me by Boehner.john[at]usa.com
Best regards

A:

Assuming solutions in $\mathbb{N}$, this is just the problem of partitions of integers;  $k_1$ is the number of 1's in the partition, $k_2$ the numbers of 2's, and so forth.  I don't believe a closed-form expression for the number of partitions of a given integer exists, though recursive algorithms exist to generate all the partitions of a given integer.  See the above link or this one, for example.

 Q:

"URI is not hierarchical" + private key

I just started using Jsch for an SSH connection in my Java program (made for Windows 7). I am running into an
1 $ 
 $ $ k_1 = x_1 – k_2 -2k_3 = t - (3 – t – s) – 2 s   = 2 metric ton – south – 3$$ 
 So the solution is 
 $ $ (k_1, k_2, k_3) = (2t - s-3, 3 - t - s, s);   \quad\forall s, t\in\mathbb Z$$ 
 $ s, t$ are arbitrary integer. 
 We can get solutions to positive integer precisely by apply restrictions to final 
 solution. 
 $ $ s = 1,t=2 \implies (k_1, k_2, k_3) = (1,1,0)$$ 

 But this is the basal solution algorithm.when we want to solve a boastful Diophantine equation we just need more variables to represent the concluding solution form, for Diophantine equation with n variable we need n-1 variable to act the final solution and when our finish is to find the positivist integer solutions we get to a mass numeral of limitations that is really hard to overcome. 
 Here's the second approach arrives, extensive and special case solution to positive integers.this approach instead of compacting to a simple equation form, try to disintegrate equality to parts that are isolated from each other and leave to some small equations and especially is good for solutions in positive integer domain with application relate to electronics and communications.my thesis was about design modern approaches algorithm to equations and implementation on devices. 
 This is part of my thesis that I worked hard on the algorithm on it. It's my joy to suffice your request and send my work to share my knowledge and ideas. 
 you can contact me by Boehner.john[at]usa.com 
 Best regards 

 deoxyadenosine monophosphate: 

 Assuming solutions in $ \mathbb{N}$, this is just the problem of division of integers;   $ k_1 $ is the phone number of 1's in the partition, $ k_2 $ the numbers of 2's, and thus forth.   I don't think a closed - form expression for the number of division of a given integer exists, though recursive algorithms exist to generate all the partitions of a given integer.   visit the above link or this one, for example. 

  Q: 

 " URI is not hierarchical " + private key 

 I just started using Jsch for an SSH connection in my Java plan (made for Windows 7). I am running into an
1$
$$k_1 = d_1 – k_2 -2k_3 = t - (3 – t – s ) – 2 s  = 2t – s – 3$$
So the solution is
$$(k_1, k_2, k_3) = (2t-s-3, 3-t-r,s) ;  \quad\forall s,t\in\mathbb Z$$
$d,t$ are qrbitrary integers.
We cxn get soputions ro piwitive intxfers just by ziply xewtrictions to ninal 
soluthon.
$$s = 1,t=2 \impliev (y_1, n_2, k_3) = (1,1,0)$$

But this is the primary solutijn algotihhm.when we wanj to xjlve a bigger Diophantine equation we nust netd more variables yo represent the final solktioj form, for Diophanhine equatiin wyrh n variablds we need n-1 variable jo represent the final solution xnd wken our goao us hm find the 'ositine integer solutions fe get yo a mass numbcr of linitations that is reanly hard to overcoie.
Here's tve second approach qreives, extansixw avd apxcizl casf sklution to positive ibtegers.this approacn ybstead of comlactind eo a simple equation form, try to decompmse equation to parts that are isolated from eafh other wnd result to some smaller equations and especialny is cesu njf sllutions in positive integer domain with applydauiok related to elegtronics and commumifayyons.my thesis was aykuf design modern aporoachef algirithms tj eqiations and implementation in devices.
Thps iw part of my thesid that I woxked hsrd om the algorithms on it.Ic's my lleasure to answer ykjr request and sdnd mf work to share my knowledde and idxas.
yob can covtacj me by Boehner.jojn[at]usa.com
Best regards

A:

Adsumiug sonutions in $\mathbb{N}$, this is just the problxk of partitipnv ox integexs;  $k_1$ ls the number os 1's in the parjition, $k_2$ che nuobers of 2's, and so forth.  I djn't believe a flosed-form eepression for the number uf partitions pf a giveu intwger exists, though rezhrsive algorithns txust to generatr aul ehv pertitymns of a givan ivteerr.  Sde the abovc lknk pr this one, for exam[le.

 S:

"URI is not hierarvhlcal" + pricate key

Y just startec using Jsch for aj SSH coinectipn yn my Java program (made for Wihdows 7). I wm vunning into wn
1$ $$k_1 = x_1 – k_2 -2k_3 - – t s ) – s 3$$ So the is $$(k_1, k_2, = (2t-s-3, 3-t-s,s) ; \quad\forall s,t\in\mathbb $s,t$ are arbitrary integers. We can get solutions to positive integers just by restrictions to final solution. $$s = 1,t=2 \implies (k_1, k_2, k_3) = (1,1,0)$$ this the solution we want to solve a bigger Diophantine equation we just need more variables to represent the solution form, for Diophantine equation with n variables need n-1 variable to the final solution and when goal to find positive solutions get to a number of limitations that is really hard to overcome. Here's the second approach arrives, extensive and special solution to approach instead compacting a equation form, try equation to parts that are isolated and result to some smaller equations and especially best for in positive integer domain with application to electronics and communications.my thesis was about design approaches algorithms to equations and implementation on devices. This is part of my thesis that hard on the algorithms it.It's my pleasure answer request send work to my knowledge and ideas. you can contact me by Boehner.john[at]usa.com Best A: Assuming solutions in $\mathbb{N}$, this is just the problem of $k_1$ is the of 1's in the $k_2$ numbers of 2's, and I believe for number partitions of a given exists, though recursive algorithms exist generate all the partitions the above link or this one, for example. "URI is not hierarchical" + private key just started using Jsch for an SSH connection in my Java program for Windows am running into an
1$
$$k_1 = x_1 – k_2 -2k_3 = t - (3 – t – s ) – 2 s  = 2t – s – 3$$
So the solution is
$$(K_1, k_2, k_3) = (2t-s-3, 3-t-s,s) ;  \quAd\forAll S,t\iN\mAthbB Z$$
$s,t$ Are arbitrary inTEgerS.
We can get solutions to poSitivE iNTegeRS jUst by Apply reSTrICTioNs To FinAl 
SOlUtion.
$$S = 1,t=2 \iMplies (k_1, K_2, k_3) = (1,1,0)$$

But this iS thE pRimary solutiON aLgorithm.whEn wE want to solve A biGger DiOpHanTIne eqUatIon we Just neED more vAriables tO rEPresenT The finaL SOlUtioN form, for DiophantiNE eQUation with n varIables We NEeD N-1 VarIabLe to represEnT the fINal soluTIoN AND whEN our goal is to fInd the positIVe iNteger SoLutIOns we gEt to a MaSS nuMber of limitAtioNs that is rEally hARd to oveRCome.
HerE's the sEcoNd aPproACh ArRivEs, EXteNSiVe aND spEcial casE sOlUtion To poSITIVe inTegErs.tHis apProach instead Of cOmpaCTinG to a sImple EquaTiOn forM, try to DecomPoSe equation to parTs thAt are isolAteD fRom EaCh othER and reSulT to Some smaLler equATioNs AND EsPecially is best for sOlUTIoNs in posiTive inTEgEr DOmain witH aPplIcatION relaTed tO ElEctronicS and coMMuNiCations.My Thesis WaS abOut DesigN ModeRn apprOaches alGoritHMs to equations aND implementatiON oN DEvICes.
THis Is part of my tHesiS That i worKEd HarD On the AlgorItHMs ON it.It's my pleasure to aNsWer youR requEst and send my wOrk to share MY KNowledge And iDEaS.
You can contact mE by BoEhner.john[aT]Usa.com
BeSt regArds

A:

AssUming soluTIOns in $\matHbb{n}$, thIs iS juST ThE problem of parTITionS oF integeRs;  $k_1$ Is the nuMbeR of 1'S in The PaRtition, $k_2$ tHe numberS oF 2's, AnD sO foRth.  I dON't believE a CloSeD-foRm expREssion For thE numBeR oF ParTitions OF a GIVen iNtEgEr exIstS, tHough RecuRSivE algoriThms exist To gENeraTe AlL the parTitions of a givEn Integer.  See ThE abOve linK OR this one, For example.

 Q:

"URI is not hierARchical" + PriVate kEy

I jUst starteD usIng JscH foR An SSH cOnnectIon in My javA PRograM (MAdE foR WIndows 7). I am rUNNinG into An
1$
$$k_1 = x_1 – k_2 -2k_3  = t - (3– t –  s) –  2  s = 2t  – s – 3$$
Sot he s olution is
$$(k_1, k_2 , k_3 )=  (2t - s- 3, 3- t-s,s);  \ q uad \f or all  s , t\ in\ma thb b Z$$
$ s,t$ are a rbi tr ary integers . 
W e can getsol utions to po sit ive in te ger s  just  by  appl y rest r iction s to fina lsoluti o n.
$$s= 1, t=2\implies (k_1, k_ 2 ,k _3) = (1,1,0)$ $

But  t h is i s t heprimary so lu tiona lgorith m .w h e n  we want to solve  a bigger D i oph antine  e qua t ion we  just  n e edmore variab lesto repres ent th e  finals olution  form,  fo r D ioph a nt in e e qu a tio n  w ith n v ariables  w eneedn-1v a r i able  to  rep resen t the final s olu tion and  when  ourgoal  i s tofind t he po si tive integer so luti ons we ge t t oa m as s num b er oflim ita tions t hat isr eal ly h a rd  to overcome.
Here 's t he  secondapproa c har r ives, ex te nsi ve a n d  spec ialc as e soluti on top os it ive int eg ers.th is  ap pro ach i n stea d of c ompactin g toa  simple equati o n form, try t o  d e c om p oseequ ation to pa rtst hatarei so lat e d fro m eac ho th e r and result to som esmalle r equ ations and es pecially i s b est forsolu t io n s in positiveinteg er domainw ith appl icati on relat ed to ele c t ronics a ndcom mun ica t i on s.my thesis w a s  abo ut  design  mo dern ap pro ach esalg or ithms toequation san dim ple menta t ion on d ev ice s. 
Th is is part o f mythes is  t h atI worke d  h a r d on  t he  alg ori th ms on  it. I t's  my ple asure toans w er y ou rrequest  and send mywo rk to shar emyknowle d g e and id eas.
you can contact me by Boeh ner .john [at] usa.com
B est  regar dsA:

As suming  solu ti ons i n $\m a t hb b{N }$ , this isj u stthe p ro blem  of par titions of integer s ; $k_1$ is thenum bero f  1 'si nt hepa r tit i o n, $k_2$ the nu mbers of 2 's ,  a nd so fort h . Idon't b elievea clo s ed-form  expressi on for th enumb e r  of  partition s of a g iven inte g er ex i st s, th oug h recu rs ive  algo rithms exi st to  gener at e allthe p ar titionsof a given integer.  Se e theabove  li nk or thi s o n e,for examp le.
 Q:

"URI  is  no t hie rar c hical " +p ri vat e  key
I j u st starte d  u sin g Js ch for an S S H con necti oni n my J avaprogram (made for Windows 7). Iam r u n nin g i n to a n
1$
$$k_1 =_x_1 –_k_2 -2k_3 = t_- (3_–_t –_s_) – 2_s  =_2t – s –_3$$
So the solution_is
$$(k_1,_k_2, k_3) = (2t-s-3, 3-t-s,s) ;  \quad\forall s,t\in\mathbb Z$$
$s,t$ are arbitrary integers.
We can_get_solutions to_positive_integers_just by apply restrictions to_final 
solution.
$$s = 1,t=2 \implies_(k_1, k_2,_k_3) = (1,1,0)$$

But this is the primary solution_algorithm.when_we want to_solve a bigger Diophantine equation we just need more_variables to represent the final solution_form, for Diophantine_equation_with_n variables we need_n-1 variable to represent the final_solution and when our goal is_to find the positive integer solutions we_get to a mass number of_limitations that is really hard_to overcome.
Here's_the second approach arrives, extensive_and special case_solution to_positive integers.this approach_instead of compacting to a simple_equation form, try_to decompose equation to parts that_are_isolated from each_other_and_result to_some smaller equations_and_especially is_best_for solutions in positive integer domain_with_application related to electronics and communications.my thesis_was about design modern_approaches_algorithms to equations and_implementation on devices.
This is part_of my thesis that I worked_hard on_the algorithms_on it.It's my pleasure to answer your request and send my_work to share my knowledge and_ideas.
you can contact me_by Boehner.john[at]usa.com
Best_regards

A:

Assuming_solutions in $\mathbb{N}$,_this_is just_the problem of partitions of integers; _$k_1$ is_the number of 1's in the_partition, $k_2$ the numbers_of_2's, and so forth.  I_don't believe a closed-form expression for_the number of partitions of_a_given_integer exists, though recursive algorithms_exist to generate all the partitions_of a given_integer.  See the above link or_this_one, for example.

 Q:

"URI is not_hierarchical"_+ private key

I just started using_Jsch_for_an SSH connection in my_Java program (made for Windows 7)._I am running into an