1+7+2+9=19, 19*91=1729 lol
Sum[Sum[Sum[
Sum[If[(x + y + z +
w)*(10*(Mod[(x + y + z + w), 10]) + ((x + y + z + w) -
Mod[(x + y + z + w), 10])/10) ==
1000*x + 100*y + 10 z + w, 1, 0]*
q^(1000*x + 100*y + 10*z + w), {x, 0, 9}], {y, 0, 9}], {z, 0,
9}], {w, 0, 9}]=
=1 + q^10 + q^810 + q^1458 + q^1729
So 1458 is also 1+4+5+8=18, 18*81=1458
810=8+1+0=09 09*90=810
10=1+0=01 01*10=10
So 1458 is another 4 digit interesting number. Probably less interesting than 1729 unless you can make it one lol! So make it!
27^2+27^2=3^6+3^6=1458
3^4+3^4+6^4=1458
6^2+5^3+6^4+1^5=1458 (related to mdZ or 2345 conjecture lol, all but a finite set of natural numbers can be written as a sum of a square, a cube, a 4th and a 5th power of other natural numbers- can you help disprove or settle this?)
Interesting can be many things of course.
So far 1458 has helped me learn things i didnt know about these places and times;
https://en.wikipedia.org/wiki/Magdalen_College,_Oxford
https://en.wikipedia.org/wiki/Cape_Verde
1458 The Turks issue a decree to protect the Acropolis after they conquer Athens. (ok at least this started better than it ended lol)
Last edited by masque de Z; 07-04-2016 at 12:13 AM.