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For The Mathematically Inclined

Anil Saigal
07/31/2017

Problem 1:

The sum of the reciprocals of two real numbers is −1, and the sum of their cubes is 4.  What are the numbers?

Problem 2:
In how many ways can 50! be expressed as a sum of two or more consecutive positive integers?

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Please send your solutions anil@lokvani.com. 

Use Problem Solutions M-080317 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani. 

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com. 

If you need clarification on any problem, please contact anil@lokvani.com. 

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Problems from 07/20/17

Problem 1:
Which term of the arithmetic sequence 2, 5, 8... is equal to 227?


Problem 2:
The sum of three consecutive numbers in an arithmetic sequence is equal 27 and their product is equal to 585. What is the largest of  the three numbers?

Congratulations to Ramachandran Balakrishna and Avanish Gowrishankar, who were the winners of the last set of puzzles.



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