java - Generate an infinite stream of tuples -

i need generate infinite stream of tuples, satisfy equation:

2 * * + b * b = c * c

i starting java 8 , unsure how achieve this. have interface tuple:

public interface tuple {     /**      * @return value of      */     int geta();      /**      * @return value of b      */     int getb();      /**      * @return value of c      */     int getc(); } 

and far have method:

public static stream<tuple> generateabctuples() {     supplier<tuple> atuple = (supplier<tuple>) generateabctuples();     stream<tuple> mylist = stream.generate(atuple)                                  .sorted();     return mylist; } 

however, unsure how satisfy above equation. on appreciated.

let's little research (using non-negative values)
2*a^2+b^2=c^2
2*a^2 = c^2 - b^2 = (c-b)*(c+b)
can see b , c must both odd or both even. anyway, right part divisible 4, left divisible 4 too, , even. condition: c >= b
let's

a = 2*p u=(c-b)/2 v=(c+b)/2 [with v>=u]      

so

b=v-u   c=v+u 8*p^2 = 4 * u * v 2*p^2 = u * v   

now can take value of p, factorize 2*p^2, find possible factors u , v, , corresponding a, b, c values (probably not unique). example:

p=0  =>  u=0, v=any value, c=b pairs solutions 2*0+k^2=k^2 p=1  =>  v=2, u=1  a=2 b=1 c=3   2*4+1=9   p=2  =>  v=8, u=1  a=4 b=7 c=9   2*16+49=81  //and second factorization:          v=4, u=2  a=4 b=2 c=6    2*16+4=36 , on... 

of course, every triplet element might negative: a=-2 b=1 c=-3 valid solution