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More about 1729 (Posted on 2012-01-04) Difficulty: 3 of 5
Much was said about 1729 a.k.a. Ramanujan number.or a taxicab number.
1729 is also a Carmichael number and the first absolute Euler pseudoprime, a sphenic number, a Zeisel number etc etc

  Please note the following (and solve):
  1. 1729 is one of four positive integers (with the others being A, B and the trivial case 1) which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:
1 + 7 + 2 + 9 = 19 ; 19*91 = 1729
Find A and B.

2. 1729= xyz, where x,y and z are integer members of an arithmetic progression.
Find these members.

3. 1729 can be expressed (in more than one way) as a sum of distinct Fibonacci numbers
List all the expressions.
 

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Answers | Comment 6 of 8 |
1. A=81=9*9
B=1458=18*81

2. 1729=7*13*19

3. 1729=1597+89+34+8+1


  Posted by Math Man on 2012-01-04 21:52:14
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