BMO1 2007 6

BMO1 2006 6

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:zap: :zap: :zap: :zap: LET’S GOOO!!! :zap: :zap: :zap: :zap:

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Brilliantly fast!

My latex skills unfortunately are pretty bad and I can’t type it that quickly.

(I in fact recall solving this problem a while back except 12n^2 was 28n^2)

That brings to question, could we change the 12n^2 to 4pn^2 where p is a prime (and not equal to 2)?

(Note that this will only work for primes in which p-1 is a QNR)
This can be generalized as any prime 1 \pmod {4} has p-1 as a QR while any prime 3 \pmod {4} has p-1 as a QNR. (Euler’s Criterion)

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