|
|
A293693
|
|
Numbers z such that x^2 + y^7 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.
|
|
2
|
|
|
33, 1094, 2219, 4097, 6283, 39063, 40156, 69985, 78157, 82221, 148109, 411772, 412865, 450834, 524289, 526475, 602413, 823575, 827639, 893527, 1347831, 2391485, 2430547, 2500001, 2502187, 2803256, 3323543, 4783001, 4787065, 5307257, 7282969, 8957953, 9036077
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
31^2 + 2^7 = 33^2 and gcd(31, 2, 33) = 1, 33 is a term.
8879827^2 + 60^7 = 9036077^2 and gcd(8879827, 60, 9036077) = 1, 9036077 is a term.
|
|
MATHEMATICA
|
z={}; Do[If[IntegerQ[(n^2 - y^7)^(1/2)] && GCD[y, n]==1, AppendTo[z, n]], {n, 9.7*10^6}, {y, (n^2 - 1)^(1/7)}]; z
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|