perplexus.info :: Just Math : AB Crossed Floor Product

AB Crossed Floor Product (Posted on 2021-12-08)

Determine positive real numbers A and B that satisfy this equation:
2*A*floor(B) = 2020, and:
3*B*floor(A) = 2021

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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from spreadsheet

| Comment 1 of 2

After unsuccessfully attempting an analytic solution, I did some spreadsheet explorations and found 3 solutions:

(A,B)

(1010/673 , 2021/3)

(-1010 , - 2021/3030)

(-505 , - 2021/1515)

Although the last two are negative, and so, don't count.

Analytically, I set A = I+x and B = J+y,

where I and J are the floors of A and B respectively, with x and y being the fractional parts.

I found: Jx - Iy = 1009/3

Edited on December 8, 2021, 7:41 am

Posted by Larry on 2021-12-08 07:17:00

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