Can fusion and fission happen at the same time, in the same place? Can fusion and fission happen at the same time, in the same place? I was talking with a friend, and he thinks that fission and fusion happen at the same time at the sun, is that true? I guess this would cause perpetual motion, then I speculated that they could happen, but in different proportions and I believed that fusion is happening in a higher proportion than fission. What do you think? 
I've searched on wikipidia, and I still found no mention to fission happening in the sun. 
 A: The Sun's energy, of course, comes from fusion.
I think there's a small and totally insignificant amount of fission going on as well.
The majority of the Sun's mass is hydrogen, and the vast majority of what isn't hydrogen is helium (with the ratio changing over billions of years as hydrogen is fused into helium). But since the Sun formed from the same nebula as Earth and the other planets, it should contain all the same elements that Earth has. According to this web page, "About 67 elements have been detected in the solar spectrum."
Thus it's very likely that the Sun contains small amounts of uranium-235. The environment is such that it can't form enough of a concentrated mass to trigger a fission chain reaction, but U-235 can, with a low probability, decay by spontaneous fission. Other very heavy isotopes can do the same thing.
I've never heard of any research that indicates that spontaneous fission actually occurs in the Sun, but given its composition it seems almost inevitable that it would, in trivial and insignificant quantities.
For all practical purposes, the answer is no, there is no significant nuclear fission in the Sun. But strictly speaking, yes, there probably is.
Even if it were significant, it wouldn't produce any kind of "perpetual motion". To do that, you'd need, for example, element A fusing into element B, and then element B fissioning back into element A. That can happen (rarely), but it can't produce net energy; if one of the reactions produces energy, the other must absorb energy.
Oh yes, also hydrogen bombs (link is to Martin Beckett's answer). The fission and fusion are both exothermic (i.e., they produce energy), but the fission applies to very heavy elements and the fusion to very light ones.
A: Fission doesn't happen in the sun. 
Elements are neatly divided at Iron, atoms smaller than this are energetically capable of fusion - they give off energy when fused. Atoms heavier than this can in theory be fissile, energy would be needed to fuse them but they give off energy when they split. These heavy atoms are only formed in a supernova where there is a lot of extra energy around to force them to fuse.
The only place that fission and fusion occur at the same time - although to different atoms - is in a thermonuclear bomb. These use a plutonium (or conceivably Uranium) fissile core to generate the heat and pressure needed to fuse hydrogen (or more commonly dueterium/tritium)
A: The sun is composed mainly of Hydrogen and Helium:

Chemically, about three quarters of the Sun's mass consists of hydrogen, while the rest is mostly helium. The remainder (1.69%, which nonetheless equals 5,628 times the mass of Earth) consists of heavier elements, including oxygen, carbon, neon and iron, among others.

Iron is at the top of the binding energy curve which separates the fissible from the fusible elements.
So no, fission is not contributing to the sun's energy output.
In order to have fusion nucleosynthesis should have happened otherwise there are no heavy fissionable elements in the star. This is supposed to happen in supernova explosions, the energy to create the heavy elements supplied by the explosion,  and these elements end up in planets like the ones in the solar system.
