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Sum three, get one (Posted on 2007-04-25)

Determine all possible positive integer solutions of this equation:

n! = a! + b! + c!

See The Solution Submitted by K Sengupta

Rating: 2.5000 (2 votes)

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Solution with explanation

Comment 4 of 4 |

with no loss in generality, assume n > c >= b >= a. Then

c! + b! + a! = n! >= (c+1)!

b! + a! >= c c!

But c = 1 = a = b does not give a solution. so c >= 2 and

b! + a! >= c c! >= 2 c! = c! + c!

so a = b = c and

c! + b! + a! = 3c!

but 3c! = n! only works if c= 2. so a=b=c=2, n=3

Posted by FrankM on 2020-04-09 11:47:30

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