1. The problem statement, all variables and given/known data Given an abelian group G with generators x and y, and relations 30x + 105y = 42x + 70y = 0, show it's cyclic and give its order. 2. Relevant equations 3. The attempt at a solution I'm guessing the proof basically involves cleverly adding 0 to 0 to show that x = ry or y = rx for some r in the integers, but I'm apparently not clever enough to find the trick. I did notice that 30 = 2*3*5, 105 = 3*5*7, 42 = 2*3*7, and 70 = 2*5*7 which is interesting, but I'm not sure how to tie it together, probably due to my weak background in number theory. Any hints?