In terms of unsolved theorems / conjectures... what would be the most accolade gaining problem to solve in modern math?
217269
Fermat's Last Theorem has been solved ashas the Four Color Theorem. The Poincare conjecture has recently been solved. Trisecting a general angle with unmarked straightedge and compass has been shown to be unsolvable (although it is possible with marked straightedge and compass).\n\nHigh on the list of open problems:\n\nRiemann Hypothesis.\nP=NP?\nTwin prime conjecture.\nAre there any odd perfect numbers?\nProof of existence of solutions to Navier-Stokes equations.
249081
one in which you have to solve the math and show your work.
438186
it has already been proved for n > 2. \n\n2^n = t^n - w^n => t^n = 2^n + w^n\n\nFamous Format's Last theorem\n\nIt need to be proved for 2\n\n4= t^2-w^2\nor (t-w)*(t+w) = 4\n\nt-w and t+w have to be both odd or both even\n\nonly solution = t-w = t+w = 2 or w = 0\nso no solution
94005
How about the discovery of pi, or the the number zero? These are crowd pleasers :), and you can find lots of material on the web, for instance:\n\nhttp://www-history.mcs.st-and.ac.uk/HistTopics/Pi_through_the_ages.html
83086
You see, it would be easier to post *exactly* what you have to do because at the moment you are not providing enough information on the problem.  For example, it seems to me that you maybe solving for integer solutions (x,y), with integers a,b,c.
567940
Sorry to say but there are no eureka moments in mathematics. There is only a couple of tips that I can give you: practice and practice smart. And focus and pay attention at class. When you practice though, dont practice using just one question book. Try different ones and try different levels of difficulty. The thing about academical mathematics is that the more you are experienced with many questions, the better you become. If you encounter a question that you cant do, ask somebody who can. Pay attention to the way of solving rather than the answer itself. All the best. Love+peace
269716
There are many undetermined ( not undefined ) mathematical quantities such as :\ninfinity - infinity\ninfinity / infinity\nzero / zero\nzero ^ zero\nzero * infinity\nas an example : (0^2)^0 = 0^0\n                (0^3)^0 = 0^0\nis that mean that 2=3 ?\nSo 0^0 is an undetermined quantity\nregarding that zero can be considered as the smallest +ve quantity we can ever have or the biggest -ve quantity we can ever have
429828
Mandelbrot Set\nWe just went over it in algebra 2/trig but it is easy enough to learn at an 8th grade level
225034
Fermat's last theorem has been solved and verified and Wiles already got the reward for it and that was some time ago.
525548
I would have to say physics, especially for a theoreticist.. If you ask me, physics has a purity to it that is not present in anything called engineering...
511912
The best way to attack proving problems in geometry is to answer and answer more proving related problem. No one can help to solve a problem. No one can help you speed up how you solve. It's you who can do that.\n\nMost of my classmates want to be good in algebra.\nBut they hate to solve algebraic proble,.\nI told them to try  answering all the questions and exercises in a book of algebra. At first, they did not believe what I have told them. Until they realize that they are becoming better and better in attacking problems in algebra.\n\nSo i think, it's up tp you if you will be good in proving geometric relations.\nI have also done it myself.\nAnd i can't believe believe that i can answer a problem with ease. It only took me a few second to answer a problem that my classmates took lots of minutes to answer.\n\nBelieve me. Solve and solve lots of problem. And you will soon realize that you will solve difficult problems with ease.
653247
Yes!!!!!!!!! Email me, and I'll try to shed more light on this. Parabolas are where my genius comes out :)
153623
Fermat claimed he had a proof 300 years ago but he\nnever demonstrated it. Andrew Wiles proved it in 1996\nbut had to use 20th century mathematics. There's an interesting book called Fermat's Enigma dedicated to\nDr. Wiles 7 year quest to prove it. There's also a \ndocumentary which has been aired on PBS which I've\nseen twice and wouldn't miss it if it came out again.
521878
The 'good news' is that this problem does not involve calculus, only number theory (or counting).  The 'bad news' is that very few students 'get it' when it comes to bases other than 10 (after all, we use base 10 numbers daily, so we tend not to think about how they work!).\n\nI think the best way to deal with this subject is to take a minute to think about "regular numbers" like 276.  Say it out loud, "Two hundred seventy six."  If you literally started with THREE numbers -- a 200, a 70, and a 6 -- and added them together, you would end up with 276.  Right?\n\nWell, picking a number apart by its digits (like the '2', the '7' and the '6' above) is exactly what you do in any base.  Except, instead of 'hundreds', 'tens' and 'ones', you have to find "powers of the new base".\n\nPowers of 10, of course, are easy.  We call them names like 'thousand' (10^3) or 'million' (10^6).  But what are the powers of, say, 8?\n\nLet's list them:\n8 raised to the 0 power?  That's 1.  Any base to the zero power is 1.  So that's nice.\n\n8 raised to the 1 power?  That's 8.  Any base raised to the one power is 'itself.'\n\n8 raised to the 2 power?  That's 64.  Any base raised to the two power is 'itself times itself.'\n\n8 raised to the 3 power?  That's 512.  As you might have guessed, that's just 8*8*8.\n\nAnd so on... we only needed those powers for your problem.  Because the given number (3175) only has four digits!\n\nLet's take each digit, starting with the 3 and working our way toward the right.  We'll multiply each digit times the power of 8 (the given base) that the digit 'stands for'.  At the end, we'll add everything up!\n\n3 times 8^3 = 3 * 512 = 1536\n1 times 8^2 = 1 * 64   = 64\n7 times 8^1 = 7 * 8     = 56\n5 times 8^0 = 5 * 1     = 5\n\nAdd them all up, now.  = 1661 (in base 10)\n\nWe've just 'converted' to base 10 this way.  Does it seem strange that the 'same' number can be written different ways using different bases?  3175 (base 8) = 1661 (base 10)\n\nThis number could be represented a zillion different ways if you keep changing the base!\n\nBut the problem asks for you to convert it to base 830.  In fact, it's unclear whether we should now convert "1661" (the n we found) or "1662" ("the integer immediately after n").\n\nLet's convert 1662 for fun, into base 830.\n\nLucky for us, the powers of 830 get BIG quickly, and we don't need more than the first couple of powers:\n\n830 ^ 0 =    1 (as always)\n830 ^ 1 = 830\n830 ^ 2 = ___ (way too BIG)\n\nAll we need to do is ask "How many times will these powers of our new base go into 1662?"  And then repeat that question with the remainder.\n\n1662 divided by 830 is "a little over 2".  (Because 830 * 2 is only 1660.)  So, the first digit of the answer is '2'.  \n\nWhat is the remainder?  Subtract:  1662 - 1660 = 2.  The remainder happens to be two.\n\nHow many times will the next-lower power of 830 go into the remainder?  Lucky for us, the next-lower power of 830 is "the 0 power", so we're thinking about 1.  How many times does 1 go into two?  Exactly twice!\n\nSo the final digit of our answer is ALSO 2.\n\nThe answer is (put the digits together): 22!\n\nNeat, huh?
601150
proof positive\nyou can find it here\nhttp://www.scifi.com/proofpositive/
658071
(m)\n\nMath Mysteries offers an effective way to teach basic skills for solving word problems like those found on state tests. Students learn how to understand the problem, collect information, solve the problem, and check their answer. Best of all, students interact with engaging characters to unravel an intriguing mystery, answering word problems every step of the way! \n\nThe mystery in Measurement revolves around a top-secret underwater mission. All communication has been lost with Outpost Omega, a research station far beneath the surface. You've been enlisted to make contact with the outpost crew. The crews on the surface ship and at the outpost will brief you on the string of mysterious events that leads to a surprising discovery.
517016
Kepler had something to say about this type of problem.\nGMT^2=4*pi^2*a^3