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

Author

Albert Lau, Jan 18 2017

Keywords

• nonn

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.

Examples

			    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.
		

Links

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

Programs

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*)