perplexus.info :: Just Math : Some Powers Sum Power

Some Powers Sum Power (Posted on 2014-03-09)

Determine all possible triplets (A,B,C) of positive integers such that:

                     A^B + B^C = C^A

Prove that there are no others.

No Solution Yet Submitted by K Sengupta

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re(2): Near Misses

Comment 3 of 3 |

(In reply to re: Near Misses by Ady TZIDON)

Indeed

10   for Tot=2 to 9999
20    for A=1 to Tot-2
30      for B=A to Tot-A-1
40         C=Tot-A-B
50         if A^B+B^C=C^A then print A;B;C
100      next
110    next
120   next

which checks all A, B and C up to a total of 9999 finds no other solution than 1,1,2 for A,B,C.

Edited on March 9, 2014, 6:55 pm

Posted by Charlie on 2014-03-09 18:55:13

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