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Search: id:A089216
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| A089216 |
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Number of triples (x,y,z) of integers such that 0<=x<=y<n, 0<=z<n, n^2=x^2+y^2-z^2. |
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+0
1
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| 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 3, 2, 2, 5, 3, 5, 4, 4, 4, 7, 4, 7
(list; graph; listen)
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OFFSET
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1,11
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COMMENT
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For any integer n>=7, there exists integers x, y, z such that 0<=x<n,0<=y<n, 0<=z<n, n^2=x^2+y^2-z^2. Hence the only functions f of the natural integers into themselves such that: f(m^2+n^2)=f(m)^2+f(n)^2 are the identity and the null function.
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PROGRAM
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(*Turbo-Pascal*) VAR nMax, n, nbt, x, y, z: integer; BEGIN write('Maximum value of n: '); readln(nMax); for n := 1 to nMax do begin write(n, ':'); nbt := 0; for y := 0 to n-1 do for x := 0 to y do for z := 0 to n-1 do begin if x*x+y*y-z*z=n*n then begin nbt := nbt+1; write('(', x, ', ', y, ', ', z, ')'); end; end; writeln(' ', nbt, '.'); end; END.
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CROSSREFS
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Sequence in context: A047679 A035050 A046819 this_sequence A102746 A123143 A128133
Adjacent sequences: A089213 A089214 A089215 this_sequence A089217 A089218 A089219
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KEYWORD
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nonn
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AUTHOR
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Roger Cuculiere (cuculier(AT)imaginet.fr), Dec 10 2003
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