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

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

Pipo found:

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

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

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

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

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

math grad - Interest: Number theory
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### 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