poppers@aecom.UUCP (Michael Poppers) (03/21/84)
Factorials are taking over the Earth! Swarms of...whoops - sorry, wrong commercial. Anyway, wouldst thou like to conquer some factorials today? 1) Find all solutions, in integers, to the equation ------------ ' 2 ' ' n! = k ' '----------' 2) Do likewise for the equation m ----- \ \ 2 / n! = k / ----- n=1 ****************** # PERITUS CLAVIS # Michael Poppers # MACHINAE VIVET # ** poppers @ AECOM ** ******************
poppers@aecom.UUCP (Michael Poppers) (03/23/84)
Here I am, catching up on net.math from the last few weeks, and what
do I see - the same problem posted by a fellow AECOMer?! I'll just have to
come up with a solution myself (once I've decrypted the "rota 13" answer and see
a different path to the solution!) - but don't hold your breath.
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PERITUS CLAVIS Michael Poppers
MACHINAE VIVIT ** The Yek-Yak **
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nike@harvard.UUCP (Nike Horton) (04/01/84)
Gur Ceboyrz: Fubj gung 1!+2!+...+a! != x^2 sbe nyy a naq x. Gur Nafjre: Fvapr a! zbq 5 = 0 sbe a>=5, 1!+2!+...a! zbq 5 = 1!+2!+3!+4! zbq 5 = 3 sbe a>=4 Shegurezber, fvapr 0^2 zbq 5= 0, 1^2 zbq 5 = 1, 2^2 zbq 5 = 4, 3^2 zbq 5 = 4, naq 4^2 zbq 5 = 1, 1!+2!+...a! pnaabg or n cresrpg fdhner vs a>=4. Sbe a<4, vg vf eryngviryl pyrne gung bhg bs 1,1+2,1+2+6, naq 1+2+6+24=32, bayl 1 naq 1+2+6 ner cresrpg fdhnerf. Guhf gur *bayl* fbyhgvbaf ner 1!=1^2 naq 1!+2!+3!=3^2. _______ Tertbel Xhcreoret Ohearq Bhg "Rherxn!" -Nepuvzrqrf POSTED BY ************************************** Nicholas Horton genrad!wjh12!harvard!nike Harvard Arts and Sciences Computer Services
poppers@aecom.UUCP (04/02/84)
Mr. Horton just posted the correct solution to the problem of 1! + 2! +...+ n! = k**2 in integers n and k. I thought that I might put the solution's logic another way: The sum of the first 4 factorials is 33, and since n! for n>4 is divisible by 10 (don't ask me why! Look up Nick's article!), higher sums will all have terminal digit 3. But all squares have terminal digit 0, 1, 4, 5, 6, or 9. ================== | PERITUS CLAVIS | Michael Poppers | MACHINAE VIVIT | ** poppers @ aecom ** ================== >