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Factorials everywhere (Posted on 2004-08-16) Difficulty: 3 of 5
The equation a!b!=c! is trivial if we allow a or b to be 0 or 1.

However, adding that 1<a<b<c, also allows trivial solutions: which? What condition should be added to disallow such solutions?

Finally, adding that condition, can you find any solution to the problem?

  Submitted by Federico Kereki    
Rating: 2.6000 (5 votes)
Solution: (Hide)
If we take c=a! and b=(c-1), the equation is trivially satisfied.

Adding the condition 1<a<b<c-1 allows the solution a=6, b=7, c=10.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPartial AnswerK Sengupta2007-08-13 03:46:11
re: More trivial solutionsCharlie2004-08-16 12:25:32
SolutionSolutionBryan2004-08-16 12:04:01
More trivial solutionsRajal2004-08-16 11:17:58
SOLUTION++++Ady TZIDON2004-08-16 10:30:42
SolutionSolution / ThoughtsEric2004-08-16 09:21:19
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