Hardest math question

 Give a hard math question,whoever gives the hardest wins 1 pi.

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Tell the ones place digit of the answer in 47^2020 (47 to the power 2020)

= 438099802556115737431390305513929910299080846721303054724290867244102190078959674422338329916868854663250199876543209876543209876543210778084848421118799657743553691358024691358024012834623580246913580246913580246913580246913580246913580246913580246913580246913580246908552872130149410582400358161781051221623581459401359400350679584549566043821693272668167717812899401051146259259259259259259259259259248913699472682162327343845477777777777777777785564111888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888828641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641976

(846 digits)

47^2020 = 434183215007800582084464629833313432997213463028142031790162934389941817152361531749423392865101127783042775532008149983519518060482930949519663149638121795202872416295812739145522994509700615306647226618087359540765214349135107679362089894164211342168269635379875790508439228216416138234651410100835324125443705547436916027270542855248844782563494224602396296774788150294451190343161171274953694315485967141538101712924698271360535659022406406174414690732522069106987538594236070694678911884034320146615722008212097281179063515114595235839817709417556360651347439437439876962705715843632246176447406389320879381162049664693856390777616037505882922819110063605914180888029140963042173782668837206935087424256560024661711771265197596532931153441173869767157297630638004361470997794318927914942334682879220252751771776960412076130773963238082682278918686175127241995371859860827101077862025748764337405557972722711156619275768970621193758506952089821559969456004928344648720199113264279326061416871431618394517278396432231925287020864370879880721024110129035472095970635614403115293458929473657234889899858779133555416652314514363365252380183624483931349687299531060302293345845787794224357886847117197487895501832997580803617092302453629654601777754586724270650566160724712904280450610591250166096587655221377333463398811277675248899783261235485771498096673374586190941760215676996596681404573880144647075042384134253772052389780529813643587079008641837155331670412436699767394884298059813018079537173769456703125997654327253677604426340848026271027645457267494966356787381046908649766470851839211086493103327479017676023669600583695815637636075165516736331546453905632150836975696591728734734736192822562161789924532432586262993837062999867782769560030820244248124795408367260506157791698326800783177586878592980501671628506864466369634428933127710370426953201285832048207120012742417229443723389630465959745548624711656940803260289775038905346723340891466250587625807078828346774306984280875916147858654084640268380534863220203952412993500480349554655691022597552396341266158246818684519518075464735250720274453462037524770418468278592733202982477921951231660639418371806919255881826940668245141634008099826562440709774090570642152196307314698325800388379184106051680558972537074868094804517442307782395478348431928697662397244812992645369660042983560728194578343588664652822781269183338504039363063376255030927153910645096344215588982736894881945652022132308101899843793056421617615202239610201492171050528013752447075235782538964327102387447811022069644768821077339233585591067761053824946136265219459776783010941567904860894497205169136723750696505517078615040283788774527884103358037560971421467308068864525914283990270060900023285822445499148394990248839416331637710070298857958776873563456915143895379764312948765021148462738533125200581579475855298377207734551592934915967087504092043593121003067798289913486390218080531745574292634860487072864026348992406402260042397634946207290281229852257082900823136705923675102625459672802972161920694445804209433368864815475038940223359649239743454903804909075297336780231075228415506277159566110810521907707443370036493950767720396904756105589725656900371379658309486907756702638378495979271973847423080919708868560834806282220400066913150668621152428529468352827318397708012313326174965707268884582811604876092912207369433582401

(3378 digits)

I don't know the answer but today we wrote the Mathematics Olympiad paper in school and this question was there!!! 

Some more of them are, 

√(1+2+3+4+5+.... 2019+2020)

And, 

(1÷2)+(1÷3)+(1÷4)+(1÷5)+.... (1÷2019)+(1÷2020)

And that's all I remember! 

Let n be any nonnegative integer.

The ones digit of 47^(4n+0) is 1.

The ones digit of 47^(4n+1) is 7.

The ones digit of 47^(4n+2) is 9.

The ones digit of 47^(4n+3) is 3.

2020=4*505+0 so the ones digit of 47^2020 is 1.

Let n be a positive integer.

1+2+3+…+n=n(n+1)/2

(1+2+3+…+2020)=2020*2021/2=2041210=2*5*43*47*101

(1+2+3+…+2020)^1/2=2041210^1/2

(1÷2)+(1÷3)+(1÷4)+(1÷5)+…+(1÷2019)+(1÷2020)

For information about this sum, use the Wikipedia page for Harmonic number.

well if you multiply 7 alot, the last number follows a pattern, e.g.

7^1=7

7^2=49

7^3=343

7^4=2401

7^5= somethingsomethingsomething7

this pattern of the last digit being 7, 9, 3, 1 isn't affected by the 10's digit at all (pwers of 17, 27, 37, 47 all end in this pattern), so dividing 2020 by 4, we get remainder 0, which is the digit 1 (our answer)

oh cool you already explained lol

https://www.youtube.com/watch?v=F_0yfvm0UoU

thanks for teaching me something

 these questions are very hard

Ok now what was the hardest??? 

Hosts vote.Put which one you think is the hardest!

I vote for @youblundered_XD 's one(s)

lol.

The thousands digit of 1210029936876168827368712638767384861700120030454560200200708076543021007227^112452415523152451455165346254

2 to the 1,000,000,000,000 power