[/quote]
,
\end{table}
x 
unit squares. Strawberries lie on some of the unit squares so that each row or column contains exactly one strawberry; call this arrangement 
.
be another such arrangement. Suppose that every grid rectangle with one vertex at the top left corner of the cake contains no fewer strawberries of arrangement 
by performing a number of switches, defined as follows:
denote the number of prime factors of 
,![\[ \sum_{n=1}^{1989} (-1)^{\Omega(n)}\left\lfloor \frac{1989}{n} \right \rfloor. \]](http://latex.artofproblemsolving.com/2/0/4/2043dca9f2ff2adfd3c8d49fa4dd278871968db0.png)
denote the set of positive integers.
such that for all 
,![\[f(mn)^2 = f(m^2)f(f(n))f(mf(n))\]](http://latex.artofproblemsolving.com/5/b/c/5bcd0f162c76b4177801933623724e576476fa88.png)
if and only if 
grid which is made up of 
unit squares and 
edges. We colour each of these edges either 
or 
.
where 
.
is the circumcenter of triangle 
is the projection of point 
onto line 
.
,
are 
,
,
,
intersects 
and 
at points 
and 
,
.
be real numbers less than 2.Then prove that 
be an acute-angled triangle and let 
,
,
be the midpoints of 
,
,
respectively. Construct a circle, centered at the orthocenter of triangle 
to intersect the circle at 
,
to intersect the circle at 
and 
to intersect the circle at 
.
.
and 
be two sequences of integers such that 
and 
for all 
.
divides 
for an infinity of integers 
such that 
for all 
Prove that 
Where 
:o
so 
and since 
is just 
therefore 
so 
Y by coolak, Math-Ninja, avaaops, potato36, lkarhat, math_swim, ironpanther29, snowstar19, Carpemath, asdf334, Laavanay_14, haha0201, LJCoder619, Bacon2387, csunllc, hdrcure, prestonh, CatsMeow12, Williamgolly, FIREDRAGONMATH16, bingo2019, anc3, tokumi, Shubhashubha, vsamc, TheDonkTonk, Problemsolving17, Lcz, Jerry122805, rf20008, aidan0626, bascar1, Abdulwahab, OlympusHero, BunnyFuzz, AnimalLover111, milkitbun, ATGY, NamePending, smartatmath, Aspiring_Mathletes, Jc426, JustinHW, peace09, Quentissential, MathWizard237, ARay10, mzeng1325, lovefractions, mathNart, thin21, snow52, ksdicecream, Mogmog8, mrmath0720, Critical, lakesiide, mathisverynice, SciBoy2000, Pi-rate, son7, Blueclay, ObjectZ, Cayle, volcanogobbler, Diamondsquid, RedFireTruck, acoderpuella, amazingxin777, Supernova283, ImSh95, Everestbaker, smarty101, rachelshi, tyseo, ThriftyPiano, samrocksnature, fuzimiao2013, tonyme.2, Lilathebee, RedFlame2112, hi.., ejlimbach, Bradygho, Aparna_J, exp-ipi-1, Mathdreams, JVAJVA, suvamkonar, evanhliu2009, nikitadas, zunaid_cnd, Eat314, Flying_Bird, centslordm, Michaelthecool, MLiang2018, NoSignOfTheta, Paul10, aayr, eagles2018, Math_lrnr, jhu08, mathking999, violin21, Jndd, HWenslawski, lc426, robotsrule123, gnidoc, EthanTAoPS, dan09, megarnie, Pi31, dbnl, Robomania_534, ycj, innout, shadow09, justJen, megahertz13, smileapple, akliu, rg_ryse, michaelwenquan, ostriches88, CastawayFly, Lamboreghini, Cygnet, Peregrine11, xiran, aaronzheng, Ethan_j, ryusei, challengeitmath, MathWhiz2493, d.d0nut, AnikaMehta, MightyDog, jgao2022, the_mathmagician, 953324, beef7, minecraft_2, RhinocerosHornbill, happymathEZ, Goddess101, NegativeZeroPlusOne, happy_k-chappie, Honestcobra, angrybird_r, P3Tan, ryanbear, MrThinker, greenplanet2050, MetalTigerMath, TheHawk, lilnutball3, elizhang101412, akpi2, Scienceiscool123, amaops1123, rohan.sp, mathmax12, peelybonehead, Cokevending56, trk08, ryanc226, thumper12, jmiao, CleverIguana, dqlam, ethancui0529, OronSH, DU4532, AlienGirl05, BabaLama, bryangyyuan, Mathbee2020, tennistiger29, lpieleanu, goldendog, Aopsauser9999, MathPerson12321, skronkmonster, yompapike, TechSavvy, Spiritpalm, Adventure10, ChuMath, tigeryong, Sedro, ultimatehero, Mango247, Emerson2023, HighWater, pearlhaas, BananaBall00, Leuy452, A21, Blue_banana4, valenbb, evt917, fura3334, Solocraftsolo, Stormbreaker7984, WizardOfChess2011, Cerberusman, lordofeverything, Exponent11, Sid77, max058lee, orangebear, Shadow_Sniper, ESAOPS, InvisibleCheetah, Math-Learner99, miles888, ranu540, Kawhi2, whslovemath, Sabburi, booking, cheltstudent, chloekyan, vsarg, Wen_Liang, PeaceLilly22, AkCANdo, FunnyKoala17, shari11, Yrock, tacocatz, PikaPika999, DDCN_2011, ahxun2006, Yiyj1, At777
Hi!
I'd like to introduce the Bogus Proof Marathon.
In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution
Use classic Marathon format:
Example posts:
Let's go!! Just don't make it too hard!
I'd like to introduce the Bogus Proof Marathon.
In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution
Use classic Marathon format:
[hide=P#]a1b2c3[/hide] [hide=S#]a1b2c3[/hide]
Example posts:
Let's go!! Just don't make it too hard!
This post has been edited 3 times. Last edited by pifinity, Mar 12, 2018, 7:40 PM
,
,
and
.
MUST equal 
?
which you did flipped the 1/2 because I guess you mistaken it for division
=
to get 
is undefined", which isn't exactly incorrect. imo it's a pretty gray area, but i'll roll with it.
.
,
.
,
.
.
.
for 
!
.
.
or 
.
.Now subtract both sides by 
.
.
.
.
.
,
because that would imply that 
(which is not given).
