[math-fun] Only two operations inserted between digits of N
25 Feb
2009
25 Feb
'09
6 a.m.
Hello MathFun, 736 = 7+3^6 2502 = 2+50^2 34425 = 3^4*425 39343 = 39+34^3 Are there many more integers N which give back N if we insert only two "operations" somewhere between the digits of N? The "operations" are +, -, *, /, ^ and the expression at the right of the equal sign must be unambiguous, of course. Best, É.
25 Feb
25 Feb
5:44 p.m.
736 = 7+3^6 2502 = 2+50^2 34425 = 3^4*425 39343 = 39+34^3
Are there many more integers N which give back N if we insert only two "operations" somewhere between the digits of N?
there are no more 5-digit solutions. the only four 6-digit solutions are: 250002 = 2 + 500 ^ 02 (if you allow leading 0's) 312325 = 31 ^ 2 * 325 344250 = 3 ^ 4 * 4250 (obviously infinitely many like this) 492205 = 49 ^ 2 * 205 erich
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Erich Friedman