Would a  mathemathical proof based on Fermat's Last Theorem be important?, even a known result?
116360
well i dont know how much there would be in the line of proofs steming from Fermats Last Theorem.\n\nbut i can tell you that Andrew Wiles (the man who proved fermats last theorem) developed a fair amount of new mathematics in the process of the proof, it is speculated that the new math he developed will be studied for hundreds of years.  his new math may lead to new lines of thinkings and ways to do proofs\n\nLook at it this way fermats last theorem was proved using the shimura taniyama conjecture...basically he proved that conjecture and said therefore Fermats Last theorem is true.  But he was able to say that anythign that happened in one world happened in another.  the math is way above my head...for now.\n\nSo yes, a new proof would be important.  It has been said that the answer to a question isnt nearly as imporant as the means to get there.  Implying the new developments made by proving something stem to new ideas and proofs...such as the new math used in the proof of Fermats Last Theorem
594792
Famous Fermat contributed to the development of modern calculus. Fermat created the modern theory of numbers. Some of his results were not proved for over a century after his death, and one of them, the Last Theorem, took more than three centuries to prove.\n\nHe also contribute to mathematical physics.
11697
b-a, at least if it is mathematics
926069
suppose it is true for some n . I do not know because you say 22 I can compute and check\n\nSo 1st step is right\n\nlet it be true for some n\n\nwe need to prove for n+1\n\n60*5^n < 6^n\nmultiply both sides by 5\n60*5^(n+1) < 6^n . 5 ...1\n\nbut 6^n. 5 < 6^n . 6 as 6^n > 0\nso 6^n. 5 < 6^(n+1) ....2\n\nfrom 1 and 2\n60.5^(n+1) < 6^(n+1)\n\n\nt QED
460848
no there doesnt. If you solve the congruences one at a time and use your solution for the previous congruence in the next one, you will eventually get the colution 1 congruent to 0 (mod7) which is obviously impossible
487623
While I have no moral compunctions about math, being that math is a science, I would seriously suggest you double-check my math (especially on the 2nd one):\n\n(x^2+9)(x+1)(x-1)\n\nx(2x^2-3x+4)-6\n\n3x^2(rad^3(x-2))\n\n25(4x+1)(4x-1)\n\n3x^2(x+10)(x-10)\n\nrad^3(4x+7)
729913
Of course. The pattern is well known, and is manifested as the binomial distribution and Pascal's triangle.\n\nIt is well formulated mathematically. There is a formula that can tell you, for example, what the 18th term is in the expansion of (a+b)^30.
480236
Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southwestern France, and a mathematician who is given credit for the development of modern calculus. With his insightful theorems Fermat created the modern theory of numbers. The depth of his work can be gauged by the fact that many of his results were not proved for over a century after his death, and one of them, the Last Theorem, took more than three centuries to prove.\n\nBy the time he was 30, Pierre was a civil servant whose job was to act as a link between petitioners from Toulouse to the King of France and an enforcer of royal decrees from the King to the local people. Evidence suggests he was considerate and merciful in his duties.\n\nSince he was also required to act as an appeal judge in important local cases, he did everything he could to be impartial. To avoid socializing with those who might one day appear before him in court, he became involved in mathematics and spent as much free time as he could in its study. He was so skilled in the subject that he could be called a professional amateur.\n\nHe was mostly isolated from other mathematicians, though he wrote regularly to two English mathematicians, Digby and Wallis. He also corresponded with French mathematician, Father Mersenne who was trying to increase discussion and the exchange of ideas among French mathematicians. One was Blaise Pascal who, with Fermat, established a new branch of math - probability theory.\n\nBesides probability theory, Fermat also helped lay the foundations for calculus, an area of math that calculates the rate of change of one quantity in relation to another, for example velocity and acceleration. In particular, he is the precursor of differential calculus with his method of finding the greatest and the smallest ordinates of curved lines, analogous to that of the then unknown differential calculus.\n\nFermat himself was secretive and, since he rarely wrote complete proofs or explanations of how he got his answers, was mischievously frustrating for others to understand. He loved to announce in letters that he had just solved a problem in math but then refused to disclose its solution, leaving it for others to figure out.\n\nFermat's passion in math was in yet another branch - number theory, the relationship among numbers. While he was studying an ancient number puzzle book, he came up with a puzzle of his own that has been called Fermat's Enigma. Mathematicians worked for over three centuries to find its answer, but no one succeeded until 1994. Andrew Wiles, an English mathematician, created a proof and published it 330 years after Fermat's death in 1665.\n\nAlthough he carefully studied and drew inspiration from Diophantus, Fermat inaugurated a different tradition. Diophantus was content to find a single solution to his equations, even if it was a fraction. Fermat was only interested in integer solutions to his diophantine equations and he looked for all solutions of the equation. He also proved that certain equations had no solution, an activity which baffled his contemporaries.\n\nHe studied Pell's equation and Fermat, perfect, and amicable numbers. It was while researching perfect numbers that he created Fermat's theorem.\n\nHe created the principle of infinite descent and Fermat's factorization method.\n\nHe created the two-square theorem, and the polygonal number theorem, which states that each number is a sum of 3 triangular numbers, 4 square numbers, 5 pentagonal numbers, ...\n\nHe was the first to evaluate the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to summing geometric series. The formula that resulted was a key hint to Newton and Leibniz when they independently developed the fundamental theorems of calculus.\n\nAlthough Fermat claimed to be able to prove all his arithmetical results, few of his proofs (if he had them) have survived. And c
51055
4Pi^2 + 5Pi^2 = 9Pi^2 is not a solution to Fermat - you're only dealing with powers of 2!\nFermat's theorem is x^n + y^n = z^n  - where n is greater 2\nCan you give us an example which makes this true where n = Pi?\n\nEdit:\nUsing Windows' own calculator-\n4^Pi = 77.880233648388115107020834778598\n5^Pi = 156.99254530886590757845919883265\n9^Pi = 995.04164489285525428416364538181
998897
Fermat lived 300 years ago and is best remembered for his last theorem which says that there are no two integers, excluding 1, that can be raised to any common power greater than 2 and summed such that the total equals the value of another integer raised to the same power ie x^n+y^n can never equal z^n where x,y,z are integers greater than 1 and n is an index greater than 2. The thing that made this famous was that though sort of obvious no one could prove it and doing so became one of the great challenges in maths for 3 centuries. It wasn't until 1994 that Andrew Wiles finally had a proof accepted as being valid.
903397
You might try asking this question under "Mathematics."
667025
You should verify this.\n_0_2_4_6_8_10_12\n0|0 0 0 0 0  0  0\n2|0 4 8 12 2 6 10\n4|0 8 2 10 4 12 6\n6|0 12 10 8 6 4 2\n8|0  2  4 6 8 10 12\n10|0 6 12 4 10 2 8\n12|0 10 6 2 12 8 4
406361
well the theorem says that a^p ≡ a(modp) where p is prime.\nequivalent to this is a^(p-1) ≡ 1(modp) by just taking the a to the other side. \n\nso we know 5^6≡1(mod7)\n\nso\n5^74 = (5^6)^12 x 5^2 ≡ 1 x 5^2 ≡ 25 ≡ 4 (mod 7)
271648
boy we carry those text books along with us\nif u want us to prove then provide the theorem plz
652164
This theorem has an amazing number of proofs but this theorem(like many other mathematical concepts) as you said was known way before pythogorean times but only to INDIANS who didnt share it on the global scale!!
987524
haha, thats crazy to ask.\n\nbasically, this was proven by andrew wiles in 1994, and resubmitted after an error was found\n\nhe developed new mathematics that will basically be the foundation of study in the coming century.\n\nthe level of mathematics that would be required to understand the proof most PhD mathematicians dont have.\n\nsorry\nwish i could be more help\nmatttlocke
500368
The links below have good info. The first briefly addresses your first question, and the second is a good brief history of the problem which provides some insight as to the difficulties encountered. I actually played around with this problem a little on an elementary level and it is interesting. Cheers.\n\nhttp://www.sciam.com/print_version.cfm?articleID=000DBA55-B698-1C71-9EB7809EC588F2D7\n\nhttp://www.geocities.com/fermatnow/flt/