So yeah, I'm looking at British Mathematical Olympiad questions, and this one has me utterly stumped. Any ideas? Find all integers x, y and z such that: And
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Originally Posted by SuperCalculus So yeah, I'm looking at British Mathematical Olympiad questions, and this one has me utterly stumped. Any ideas? Find all integers x, y and z such that: And Write the first equation as . Then clearly both x and y–z must be 1 or –1. Is that enough of a hint?
"Then clearly both x and y–z must be 1 or –1." How the hell did you get that? O_o
Originally Posted by satx "Then clearly both x and y–z must be 1 or –1." How the hell did you get that? O_o What other integers could make 2 when squared and added?
Oh, my bad. Didn't see the "integers" part.
Originally Posted by Opalg Write the first equation as . Then clearly both x and y–z must be 1 or –1. Is that enough of a hint? Yeah, I reckon I've got it providing that is true, but can you tell me how you got to that equation? (I understand how it can only be 1 or -1)
Originally Posted by SuperCalculus Originally Posted by Opalg Write the first equation as . Then clearly both x and y–z must be 1 or –1. Is that enough of a hint? Yeah, I reckon I've got it providing that is true, but can you tell me how you got to that equation? (I understand how it can only be 1 or -1) If then . If you're aiming to do olympiad questions then you ought to be able to factorise .
Originally Posted by Opalg If then . If you're aiming to do olympiad questions then you ought to be able to factorise . Ugh, I knew it was something obvious. I was thinking in all these complicated terms, and all I had to do was basic rearranging >.>
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