perplexus.info :: Numbers : Cube Difference Deduction II

Cube Difference Deduction II (Posted on 2022-10-22)

Consider these nine positive integers:
987654321, 98765432, 9876543, 987654, 98765, 9876, 987, 98 and 9

Determine how many of these are expressible as the difference of cubes of two integers.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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soln

| Comment 1 of 3

The difference of two cubes may be expressed as:

(n+m)^3 - n^3 = m^3+3 n m^2 + 3 n^2 m

I wrote a little program to check if each difference "d" above could be given by this formula for some m and n. I searched n from 0 to d^(1/2) and m from 1 to d^(1/3). (Not elegant, but gets the job done.) I found only one match: n=3 and m=2:

5^3 - 3^3 = 98

Edited on October 22, 2022, 11:13 pm

Posted by Steven Lord on 2022-10-22 23:00:35

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