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 More about 1729 (Posted on 2012-01-04)
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.

 Submitted by Ady TZIDON Rating: 5.0000 (3 votes) Solution: (Hide) 1. 9*9 = 81 18*81 = 1258 19*91=1458 2. 1729 = 7*13*1 3. There are 20 solutions, - all distinct numbers: 1597+89+34+8+1 = 1729 1597+89+34+5+3+1 = 1729 1597+89+21+13+8+1 = 1729 1597+89+21+13+5+3+1 = 1729 etc... 10 additional solutions might be accepted, once you allow duplicity of number 1.

Comments: ( You must be logged in to post comments.)
 Subject Author Date correct a typo Ady TZIDON 2017-06-21 09:48:38 re 2. broll 2012-01-05 02:16:11 Answers Math Man 2012-01-04 21:52:14 re(3): computer solution Charlie 2012-01-04 15:03:09 re(2): computer solution Daniel 2012-01-04 14:31:42 re: computer solution Jer 2012-01-04 13:43:55 computer solution Charlie 2012-01-04 13:09:53 Solutions Jer 2012-01-04 11:27:31
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