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.