perplexus.info :: Just Math : Arithmetic Triplet Ascertainment

Arithmetic Triplet Ascertainment (Posted on 2016-01-03)

F(n) denotes the largest prime divisor of a positive integer n.

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

A, B and C are in arithmetic sequence, and:
F(A*B*C) ≤ 3

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

These three sets form the basis of an infinite number of sets:
(1, 2, 3) (2, 3, 4) (2, 9, 16)
multiply any one of these three sets by any number that's a product of powers of 2 and 3, and you get another set.
For an explanation, refer to the heuristic solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	Heuristic solution	Charlie	2016-01-03 10:57:44

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