Solving equation using mathematica

[76Ahmad]

Hello every one, I need help please...

How to write in mathematica to solve an equation of x and y that is equal to 0,
(i.e. y^4+2y^2x^2-15x=0)
and let the program try all the value of x=0,1,2,3,...,10000.
and all the value of y=0,1,2,3,...,100.

The program should start with x=0 and try all the 100 value of y,
and then go to the next x.

Please help..thanks

 

[jackmell]

How about just some For loops:

For[y = 0, y <= 10000, y++,
 For[x = 0, x <= 100, x++,
  If[y^4 + 2 y^2 x^2 - 15 x == 0,
    Print["My x: ", x, " my y: ", y];
    ];
  ]
 ]

or FindInstance does this but I'm not sure if we can assume the function is attempting the solutions in the order you wish.

FindInstance[
 y^4 + 2 y^2 x^2 - 15 x == 0 && 0 <= x <= 10000 && 0 <= y <= 100, {x, 
  y}, Integers]

 

[76Ahmad]

I tried the the first one and the out put was:

My x: 0 my y: 0

I do not know if its checked all the values correctly?
how to make it print for example on each 50x

x=50 no solutions
x=100 no solutions
x=150 no solutions
.
.
.

 

[Bill Simpson]

Perhaps you can learn how to use If and Mod to print diagnostic messages.

In[1]:= numsolutions=0;
For[y=0,y<=10000,y++,
For[x=0,x<=100,x++,
If[y^4+2 y^2 x^2-15 x==0,numsolutions++;Print["My x: ",x," my y: ",y];];
If[Mod[y,50]==0&&Mod[x,50]==0, Print["y=",y," x=",x, " ", numsolutions," solutions"]];
]
]

From In[1]:= My x: 0 my y: 0
From In[1]:= y=0 x=0 1 solutions
From In[1]:= y=0 x=50 1 solutions
From In[1]:= y=0 x=100 1 solutions
From In[1]:= y=50 x=0 1 solutions
From In[1]:= y=50 x=50 1 solutions
From In[1]:= y=50 x=100 1 solutions
From In[1]:= y=100 x=0 1 solutions