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Cyclic recursive summation (Posted on 2021-07-16) Difficulty: 5 of 5
Let N be the set of positive integers. Find all functions f:N->N that satisfy the equation

fabc-a(abc) + fabc-b(abc) + fabc-c(abc) = a + b + c

for all a, b, c ≥ 2.

(Here f1(n) = f(n) and fk(n) = f(fk-1(n)) for every integer k greater than 1)
(Also note: abc is the product a·b·c and not the concatenation 100a+10b+c)

No Solution Yet Submitted by Danish Ahmed Khan    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Further thoughts (4)FrankM2021-08-21 13:17:18
Approach for expanding into simple casesFrankM2021-08-17 16:23:08
No fixed point for arguments of interest FrankM2021-08-16 22:06:16
No fixed point for arguments of interest FrankM2021-08-16 22:06:11
Either no solution or an infinite number of solutions FrankM2021-08-16 21:56:11
Further thoughts (3)FrankM2021-08-05 11:58:15
Fallacy?FrankM2021-08-04 20:50:58
Further thoughts (2)FrankM2021-08-04 20:28:44
ThoughtsFrankM2021-08-04 10:26:12
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