I am trying to answer this problem: https://brilliant.org/community-problem/primeprimeprime/?group=0jEjslvgEVDa

The answer should be 5. I think because p^2 is congruent to 1 modulo 4 (for p >= 3). From the equation: p^2 - 2q^2 = 1 and so... p^2 - 1 = 2q^2 .... 2q^2 is divisible by 4 and so q^2 is even and sqrt of q^2 must be even but no prime except 2 satisfies this...

P.S. Do you have any advice on how to solve level 4 or 5 problems?.... I sometimes (in despair) use trial and error method....

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TopNewestThanks, I've updated the answer accordingly. Can you add a solution to it? – Calvin Lin Staff · 3 years ago

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