A281224 Integer c such that (a^3 + b^3 - c^3)^2 = 1 where a,b,c are integers greater than 2.

9, 12, 103, 144, 150, 172, 249, 495, 505, 577, 729, 738, 904, 1010, 1210, 1544, 1852, 1988, 2304, 2316, 3097, 3753, 4184, 5262, 5625, 5640, 6081, 6756, 8657, 8703, 9791, 9953, 11664, 11682, 12884, 14258, 16849, 18649, 21279, 21609, 21630, 24987, 29737, 31615

Offset

1,1

Comments

a^3 + b^3 = c^3 has no nontrivial integer solution, this list gives the "near misses" which satisfy a^3 + b^3 = c^3 +- 1.

If a (or b) = 1, then b (or a) = c will always satisfy a^3 + b^3 = c^3 + 1 (trivially).

If any of a,b,c is 0, the equation can be reduced to x^3 + y^3 = 1^3 (possibly taking negative values), which has no nontrivial solutions.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..200

Example

    a    b    c
  ---  ---  ---
    6    8    9
    9   10   12
   64   94  103
   71  138  144
   73  144  150
  135  138  172
E.g.: 135^3 + 138^3 = 172^3 - 1.

Mathematica

n = 500;
Do[If[a // IntegerQ, (*{a, b, c}*)c // Sow], {c, n}, {b, c/2^(1/3) // Ceiling, c - 1}, {a, ({-1, 1} + c^3 - b^3)^(1/3)}] // Reap // Last // Last(*//TableForm*)

Crossrefs

Sequence in context: A246916 A188001 A273614 * A050236 A193995 A070607

Adjacent sequences: A281221 A281222 A281223 * A281225 A281226 A281227

Keyword

nonn

Author

Albert Lau, Jan 18 2017

Status

approved