/sci/ - Science & Math

/sci/entist gentlemen, I invented a potentially harder problem when trying to solve an easier one.

Let <span class="math"> p_1, ... p_k [/spoiler] be distinct primes. Are there rational numbers <span class="math"> a_1, ... a_k [/spoiler] (besides the obvious case of them being zero) so that

<span class="math"> a_1 \sqrt{p_1} + ... a_k \sqrt{p_k} = 0 [/spoiler]

It's obviously impossible when <span class="math"> k \leq 4 [/spoiler]. But how about the rest?

Besides that, bitching about maths thread, I guess.