Problems & Puzzles: Puzzles Puzzle 284. A+B=C | A.B.C = pk# This week I tried to find solutions to the simple equation A+B=C such that A.B.C = pk# Example: 247 + 110 = 357 ↔ 13.19 + 2.5.11 = 3.7.17 (using the first 8 consecutive primes) As a matter of fact I have obtained all the solutions using k consecutive primes for 3<=k<=13 (except for k=12)
Questions: 1. Can you extend the Table? 2. Can you develop a smart approach in order to calculate the solutions for a given k value? 2. Would you expect to exist solutions for 'large' values of k? If so, please find a solution for a k larger than 50. Contributions came from Luke Pebody and Adam Stinchcombe Pebody wrote:
*** Stinchcombe wrote:
*** So, it seems that no more solutions will ever come... ***
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