Concatenation: 2016 || x || 2016 = y^4

 
  2016 \; || \; x \; || \; 2016 \; = \; y^4
 

Pipo found:

  670136^4 = \underline{2016}7487489586816418\underline{2016}
  2118998^4 = \underline{2016}146968881949179619\underline{2016}
  3768502^4 = \underline{2016}8565058520405383459\underline{2016}
  6701002^4 = \underline{2016}31782854939948983843\underline{2016}
  6701114^4 = \underline{2016}45263421491436385027\underline{2016}
  6701386^4 = \underline{2016}78004754442134244643\underline{2016}
  6701498^4 = \underline{2016}91487638613107773955\underline{2016}

11916002^4 = \underline{2016}147351972193015372531\underline{2016}
11916114^4 = \underline{2016}223153130012417513811\underline{2016}
11916386^4 = \underline{2016}407250554804259855859\underline{2016}
11916498^4 = \underline{2016}483059041032759645267\underline{2016}
11917252^4 = \underline{2016}993468235783560575410\underline{2016}

21189752^4 = \underline{2016}0601969095669644658082\underline{2016}
21189864^4 = \underline{2016}1028213880930150389154\underline{2016}
21190136^4 = \underline{2016}2063407927071992399266\underline{2016}
21190248^4 = \underline{2016}2489675885873813378466\underline{2016}
21191002^4 = \underline{2016}5359548602430537222211\underline{2016}
21191114^4 = \underline{2016}5785868825478787222051\underline{2016}
21191386^4 = \underline{2016}6821246080996544247619\underline{2016}
21191498^4 = \underline{2016}7247589480320208695587\underline{2016}

37681114^4 = \underline{2016}02045833974143497214275\underline{2016}
37681386^4 = \underline{2016}07866930475177138135395\underline{2016}
37681498^4 = \underline{2016}10263889203630540490819\underline{2016}
37682252^4 = \underline{2016}26401114076878328839858\underline{2016}
37682364^4 = \underline{2016}28798238070819560255922\underline{2016}
37682636^4 = \underline{2016}34619913900724291192498\underline{2016}
37682748^4 = \underline{2016}37017111178790845536690\underline{2016}
37683502^4 = \underline{2016}53155942039020703483987\underline{2016}
37683614^4 = \underline{2016}55553304593539790008819\underline{2016}
37683886^4 = \underline{2016}61375559790751760960851\underline{2016}
37683998^4 = \underline{2016}63772995634258197933811\underline{2016}
37684752^4 = \underline{2016}79913432588019161416866\underline{2016}
37684864^4 = \underline{2016}82311033718943197410466\underline{2016}
37685136^4 = \underline{2016}88133868321899833377954\underline{2016}
37685248^4 = \underline{2016}90531542746673408619682\underline{2016}

67007636^4 = \underline{2016}030907567235996890291378\underline{2016}
67007748^4 = \underline{2016}044386390918559670332850\underline{2016}
67008502^4 = \underline{2016}135129516607066631537827\underline{2016}
67008614^4 = \underline{2016}148608862892862750559939\underline{2016}
67008886^4 = \underline{2016}181344699551400484109731\underline{2016}
67008998^4 = \underline{2016}194824277573207211179971\underline{2016}
67009752^4 = \underline{2016}285572481646898465420706\underline{2016}
67009864^4 = \underline{2016}299052582291436469511586\underline{2016}
67010136^4 = \underline{2016}331790250974560118076834\underline{2016}
67010248^4 = \underline{2016}345270583363754547815842\underline{2016}
67011002^4 = \underline{2016}436023866012099102904835\underline{2016}
67011114^4 = \underline{2016}449504721043523111424483\underline{2016}
67011386^4 = \underline{2016}482244221819582875005187\underline{2016}
67011498^4 = \underline{2016}495725308604309288052963\underline{2016}
67012252^4 = \underline{2016}586483670016779686177714\underline{2016}
67012364^4 = \underline{2016}599965279463234343486130\underline{2016}
67012636^4 = \underline{2016}632706612400581697082290\underline{2016}
67012748^4 = \underline{2016}646188453608984899078834\underline{2016}
67013502^4 = \underline{2016}736951893975057216801843\underline{2016}
67013614^4 = \underline{2016}750434257864687692259027\underline{2016}
67013886^4 = \underline{2016}783177423031675385870643\underline{2016}
67013998^4 = \underline{2016}796660018691900707455955\underline{2016}
67014752^4 = \underline{2016}887428538201054555714722\underline{2016}
67014864^4 = \underline{2016}900911656562006543680674\underline{2016}
67015136^4 = \underline{2016}933656654026988602307746\underline{2016}
67015248^4 = \underline{2016}947140004167181899121826\underline{2016}

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

One Response to Concatenation: 2016 || x || 2016 = y^4

  1. pipo says:

    The sixth powers up to 10^8:

    355434^6 = 2016293798720667315213857729342016
    2421684^6 = 201699505964832514254829487897143382016
    7657934^6 = 201683195769270105698008442487308011902016
    11240434^6 = 2016965545864408535236183775875175590782016
    16497934^6 = 20164031687531632568365863249603389780862016
    16498316^6 = 20166833167763592074227307882119566370902016
    24215434^6 = 201629253608267447239025789641567348549182016
    24215816^6 = 201648338646146425021880447945833570602582016
    24216684^6 = 201691710245108985438240440414694267979862016
    35542934^6 = 2016135193390755508089163366361820125121342016
    35543316^6 = 2016265208150532805464610254526056342030422016
    35544184^6 = 2016560660333919961602138208276660808552022016
    35544566^6 = 2016690697957455185762561855061660798599742016
    35545434^6 = 2016986202096700428904874296850720995232702016
    52170434^6 = 20162607574160099897000819668969065460776702016
    52170816^6 = 20163493392792728917075976293618695405375062016
    52171684^6 = 20165506315909515941096148720309739313207382016
    52172066^6 = 20166392240667608498065394189157216780944382016
    52172934^6 = 20168405404939674579246856010846634543888062016
    52173316^6 = 20169291435833401914709700173241436097263702016
    76574184^6 = 201601734878761563525986567922662656412192342016
    76574566^6 = 201607769248505963120090562685545370904959422016
    76575434^6 = 201621481412636921208359493377812128776873022016
    76575816^6 = 201627516274922621143928945695400724230278742016
    76576684^6 = 201641229558267732735649367401772687832303702016
    76577066^6 = 201647264913126894511914034952772457058848062016
    76577934^6 = 201660979315759240405206723183102303265984382016
    76578316^6 = 201667015163224027096409180648691271578167382016
    76579184^6 = 201680730685216691668278265454324179140415062016
    76579566^6 = 201686767025319267923725324693201932475736702016

    (625 (mod 1250) plus or minus 191)^6 is 2016 mod 10000

    pipo

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s