286 Mr. Drach on Fermat's Undemotistrated Theorem, 



of that mysterious power which appears to emanate from the 

 solar orb. 



33. Admitting the imperfect character of the results which 

 I have endeavoured to record as faithfully as possible, I can- 

 not but regard them as important, and they appear to point' to 

 some general law, which is probably applicable to those phae- 

 nomena which Moser has described, and which are in all pro- 

 bability acting a grand part in the mutations of the universe^ 

 The same power which we detect changing the film of chloride 

 of silver on the photographic paper, has been in action for 

 countless ages on the earth's surface ; and by pursuing with 

 due care the investigation, we may be enabled to proceed, 

 step by step, into the great laboratory of nature, and discover 

 the various causes which have been in operation on the con- 

 solidated masses of this globe, and which are producing mul- 

 tifarious chemical changes, to the excitation of which are due 

 the great magnetic phaenomena which are exciting so much 

 the attention of philosophers. V i v. ''" -^ ™ \ % '^ ^/ t^ v iji 



September 11, 1845. - .Iifhinrn. ,y .rli In f>nayc9nfh oflt 



W 



. __. — ■, ■ .(it 



XLIII. Proof of Fermat's Undemonstrated Theorem, thc^t 

 ^n ^ yn -- ^n ^g Qj^iy possible iti 'whole numbers "when w = 1 

 or 2. By S. M. Drach, Esq., F.R.A.S. 



To the Editors of the Philosophical Magazine and Journal, 



Gentlemen, ^^j s\<\h?m<i^s> ei aons-rsfllh ^Ai 



' E may evidently regard k, y and z as mutually prime, 

 for a divisor common to two must enter the third, if 

 an integer solution be possible, .*. two are odd and one even. 



o^tT ZJ ?-n ^- "trioa. S^ '* ■, '^■■. ,-1-1, , »i ' r^'^^ j]*JL>m^::i>;j/p 

 By the rules 01 this analysis (buler s Algebra, pt. 2. ch. xii.), 



it appears that if 



l = a-p- + 2 ( ^ 1.2. .2f = A,)^-^'^' 



and ''« 



Y = C" 2'" + S A j q»-^ip^i cf^-i a*, '^ 



that « Z2 - c Y2 = {ap^ - c (fY . 



Put therefore a—%, Z=2;^, c=j/, ¥=3/"* .'.,v=^zp^ — cq% 

 and «»« =2»«_p'»+ SAip'*-2'52<^w-iy^ or 



. ... .... . l«:p»(l + ..SA.Y^i^)'); -' ■ -. .I>ho 



atoibiuipid e 82'3f mum ,:yi«u|Vj ^P ^^ 'fos ea.tejbc«prd ow) 



Hi fttn—i /4 



a""-' r. 



