perplexus.info :: Numbers : Algebra busters

Algebra busters (Posted on 2020-04-22)

Find the number of solutions to the system of equations:

k₁+k₂+k₃+...+k_n=5n-4
1/k₁+1/k₂+1/k₃+...+1/k_n=1

where k₁,k₂,k₃,...,k_n and n are positive integers.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Puzzle Answer

Comment 6 of 6 |

There are precisely 3 valid solutions, and these are:

S1) {n|k1} = {1|1}

S2) {n| k1, k2, k3} = {3 | 2,3,6}

S3) {n| k1, k2, k3, k4} = {4 | 4, 4, 4, 4}

Posted by K Sengupta on 2022-05-25 03:06:25

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